Operating a multi-dimensional array of qubit devices

ABSTRACT

In some aspects, a quantum computing system includes a multi-dimensional array of qubit devices. Coupler devices reside at intervals between neighboring pairs of the qubit devices in the multi-dimensional array. Each coupler device is configured to produce an electromagnetic interaction between one of the neighboring pairs of qubit devices. In some cases, each qubit device has a respective qubit operating frequency that is independent of an offset electromagnetic field experienced by the qubit device, and the coupling strength of the electromagnetic interaction provided by each coupler device varies with an offset electromagnetic field experienced by the coupler device. In some cases, readout devices are each operably coupled to a single, respective qubit device to produce qubit readout signals that indicate the quantum state of the qubit device.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/035,547, filed May 10, 2016, entitled “Operating a Multi-DimensionalArray of Qubit Devices,” which is a 371 national stage of InternationalApplication No. PCT/US2015/018152, filed Feb. 27, 2015, which claimspriority to U.S. Provisional Patent Application No. 61/946,390, filedFeb. 28, 2014, entitled “Waveguide Array for Quantum Processors;” U.S.Provisional Patent Application No. 61/946,545, filed on Feb. 28, 2014,entitled “Quantum Processor Cell Architectures;” U.S. Provisional PatentApplication No. 62/032,864, filed on Aug. 4, 2014, entitled “QuantumProcessor Control Architecture;” and U.S. Provisional Patent ApplicationNo. 62/033,022, filed on Aug. 4, 2014, entitled “Quantum ProcessorSubstrate.” All above-referenced priority documents are incorporatedherein by reference.

TECHNICAL FIELD

The subject matter described here relates to quantum computing.

BACKGROUND

Quantum computing generally involves storage or processing ofinformation in quantum mechanical states of light or matter. Informationstored in these systems can display the quantum properties of thestorage medium. These properties are different from classical Newtonianlaws of physics that govern classical computing hardware.

Significant evidence shows that the quantum computing paradigm allowscertain advantages; for example, some problems can be solved by aquantum computer using exponentially fewer resources (e.g., time, memorysize, energy) than would be used by the best known classical algorithmsand computing systems.

SUMMARY

In a general aspect, a quantum computing system includes amulti-dimensional array of qubit devices.

In some aspects, qubit control signals are received in amulti-dimensional array of qubit devices. Each qubit device has arespective qubit operating frequency that is independent of an offsetelectromagnetic field experienced by the qubit device. The qubit controlsignal received by each qubit device is configured to manipulate aquantum state of the qubit device. Coupler control signals are receivedat coupler devices. The coupler devices reside at intervals betweenneighboring pairs of the qubit devices in the multi-dimensional array.The coupler control signal received by each coupler device is configuredto produce an electromagnetic interaction between the neighboring pairof qubit devices that the coupler device resides between. A couplingstrength of the electromagnetic interaction produced by each couplerdevice is influenced by an offset electromagnetic field experienced bythe coupler device.

In some aspects, qubit control signals are received in amulti-dimensional array of qubit devices. Each qubit device has arespective qubit operating frequency that is independent of an offsetelectromagnetic field experienced by the qubit device. The qubit controlsignal received by each qubit device is configured to manipulate aquantum state of the qubit device. Qubit readout signals are produced atreadout devices associated with the multi-dimensional array of qubitdevices. Each readout device is operably coupled to a single, respectivequbit device. Each qubit readout signal is produced by one of thereadout devices based on an electromagnetic interaction between thereadout device and the respective qubit device.

In some aspects, qubit control signals are received at a quantumprocessor cell that includes a multi-dimensional array of qubit devices.The multi-dimensional array includes sub-arrays associated with separatefrequency bands. The qubit devices in each sub-array have a qubitoperating frequency within the frequency band associated with thesub-array. The qubit control signal received by each qubit device isconfigured to manipulate a quantum state of the qubit device. The qubitcontrol signals are communicated to respective qubit devices in thequantum processor cell.

The details of one or more example implementations are provided in theaccompanying drawings and the description below. Other features,objects, and advantages of the subject matter will be apparent from thedescription and drawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of an example quantum computing system.

FIG. 2 is a schematic diagram of an example quantum computing system inwhich a quantum processor cell (QPC) includes an electromagneticwaveguide system.

FIGS. 3A-3E show aspects of example devices that may be housed in aquantum processor cell; FIG. 3A shows an equivalent circuit of a portionof an example device array; FIG. 3B shows an example transmon device;FIG. 3C shows an example fluxonium device; FIG. 3D shows an equivalentcircuit for the transmon device shown in FIG. 3B; FIG. 3E shows anequivalent circuit for the fluxonium device shown in FIG. 3C.

FIGS. 4A-4E show example attributes and operations of devices that maybe included in an example quantum processor cell; FIG. 4A shows anexample energy level diagram for a qubit device; FIG. 4B shows anexample frequency diagram for a readout device; FIG. 4C shows an exampleenergy level diagram with a coupler device in its OFF state; FIG. 4Dshows an example energy level diagram with a coupler device in its ONstate; FIG. 4E shows an example coupler control signal.

FIGS. 5A-5B are schematic diagrams of example device arrays arrangedwithin an electromagnetic waveguide system that includes a 2D lattice ofintersecting waveguides.

FIGS. 6A-6B show aspects of an example electromagnetic waveguide systemthat includes a 2D lattice of intersecting waveguides; FIG. 6A shows aportion of an interior volume of an example electromagnetic waveguidesystem; FIG. 6B shows dimensions of an example waveguide interval.

FIG. 7 shows electromagnetic properties at example waveguideintersections in a 2D lattice of intersecting waveguides.

FIG. 8 shows a portion of an interior volume of another exampleelectromagnetic waveguide system that includes a 3D lattice ofintersecting waveguides.

FIG. 9 shows aspects of an example quantum processor cell (QPC) thatincludes an electromagnetic waveguide system.

FIGS. 10A-10B show aspects of the signal board in the example QPC ofFIG. 9; FIG. 10A is a side cross-sectional view; FIG. 10B is aperspective view.

FIGS. 11A-11E show aspects of the example QPC of FIG. 9; FIG. 11A showsan exploded view of a portion of the example QPC; FIG. 11B is a sidecross-sectional view of the portion illustrated in FIG. 11A; FIG. 11C isa plan view of the portion illustrated in FIG. 11A; FIG. 11D is aperspective view of the electromagnetic waveguide system in the exampleQPC of FIG. 9; FIG. 11E is a zoomed-in view of a portion of FIG. 11D.

FIGS. 12A-12B show aspects of example pass-through structures in asection of an example electromagnetic waveguide system.

FIGS. 13A-13G show an example process for assembling the example QPC ofFIG. 9.

FIG. 14A shows a portion of an interior volume of an exampleelectromagnetic waveguide system that includes a 3D lattice ofintersecting waveguides; FIG. 14B illustrates electromagnetic propertiesat an example waveguide intersection in a 3D lattice of intersectingwaveguides.

FIG. 15 shows an example electromagnetic waveguide system that includesa 3D lattice of intersecting waveguides.

FIGS. 16A-16F show aspects of an example quantum computing system thatincludes an electromagnetic waveguide system. FIG. 16A is a topcross-sectional view of an example quantum processor cell (QPC) at Z=0;FIG. 16B is a side cross-sectional view of the example QPC at Y=0 andY=±4; FIG. 16C is a top cross-sectional view of the example QPC at Z=+1;FIG. 16D is a top cross-sectional view of the example QPC at Z=−1; FIG.16E is a side cross-sectional view of the example QPC at Y=±1 and Y=±3;and FIG. 16F is a side cross-sectional view of the example QPC at Y=±2.

FIGS. 17A-17B show aspects of an example quantum computing system thatincludes a signal delivery subsystem and an electromagnetic waveguidesystem; FIG. 17A is a schematic diagram showing an example signal flow;FIG. 17B is a perspective view showing aspects of components representedin FIG. 17A.

FIGS. 18A-18C show examples of input and output connector hardware foran example quantum processor cell; FIG. 18A is a perspective view of anexample base portion of an electromagnetic waveguide system withvertical interconnects; FIG. 18B is a perspective view of an exampleelectromagnetic waveguide system showing a lid portion with verticalinterconnects; FIG. 18C shows a perspective view of internal componentsof the example electromagnetic waveguide system shown in FIG. 18B.

FIG. 19 shows aspects of an example device array in an example quantumprocessor cell.

FIGS. 20A-20E show examples components of an example signal deliverysubsystem; FIG. 20A is a side view of an example system; FIG. 20B is aperspective view of an example input interconnect plate; FIG. 20C is aperspective view of an example output interconnect plate; FIG. 20D is aperspective view of an example input signal processing system; FIG. 20Eis a perspective view of an example output signal processing system.

FIGS. 21A-C are diagrams showing example operating frequencies fordevices in a quantum processor cell; FIG. 21A is a frequency spectrumplot that indicates example operating frequencies of qubit devices andreadout devices; FIG. 21B is a frequency difference plot that indicatesdifferences between the operating frequencies shown in FIG. 21A; FIG.21C shows an example device array based on the operating frequenciesshown in FIG. 21A.

FIGS. 22A-C are diagrams showing other example operating frequencies fordevices in a quantum processor cell; FIG. 22A is a frequency spectrumplot that indicates example operating frequencies of qubit devices andreadout devices; FIG. 22B is a frequency difference plot that indicatesdifferences between the operating frequencies shown in FIG. 22A; FIG.22C shows an example device array based on the operating frequenciesshown in FIG. 22A.

FIG. 23A is a block diagram of an example quantum computing system 2300that includes multiple temperature stages and multiple operatingdomains.

FIG. 23B is a flowchart showing an example process for operating aquantum computing system.

FIG. 24 is a flowchart showing an example process for delivering controlsignals to a quantum processor cell.

FIG. 25 is a block diagram showing an example process for deliveringcontrol signals to a quantum processor cell.

FIG. 26 is a block diagram showing an example process for deliveringqubit readout signals from a quantum processor cell.

FIG. 27 is a block diagram showing an example process for deliveringcontrol signals to a quantum processor cell.

FIG. 28 is a block diagram of an example quantum computing system.

DETAILED DESCRIPTION

FIG. 1 is a schematic diagram of an example quantum computing system100. The example quantum computing system 100 shown in FIG. 1 includes acontrol system 110, a signal delivery system 106, and a quantumprocessor cell 102. A quantum computing system may include additional ordifferent features, and the components of a quantum computing system mayoperate as described with respect to FIG. 1 or in another manner.

The example quantum computing system 100 shown in FIG. 1 can performquantum computational tasks and algorithms. In some implementations, thequantum computing system 100 can perform quantum computation by storingand manipulating information within individual quantum states of acomposite quantum system. For example, qubits (i.e., quantum bits) canbe stored in and represented by an effective two-level sub-manifold of aquantum coherent physical system. The formation of composite systems forquantum computing can be achieved by couplings between the individualphysical qubits, for example, to perform conditional quantum logicoperations. In some instances, the couplings between physical qubits canbe rendered in a manner that allows large-scale entanglement within thequantum computing device. Control signals can manipulate the quantumstates of individual qubits and the couplings between qubits. In someinstances, information can be read out from the composite quantum systemby measuring the quantum states of the individual qubits.

In some implementations, the quantum computing system 100 can operate ina fault-tolerant regime. For example, fault-tolerance may be achievedthrough the use of carefully engineered dissipation and redundantencodings. In some example gate-based models for quantum computing,fault-tolerance can be achieved by applying a set of high-fidelitycontrol and measurement operations to the qubits. For example,topological quantum error correction schemes can operate on a lattice ofnearest-neighbor-coupled qubits. In some instances, these and othertypes of quantum error correcting schemes can be adapted for a two- orthree-dimensional lattice of nearest-neighbor-coupled qubits, forexample, to achieve fault-tolerant quantum computation. The lattice canallow each qubit to be independently controlled and measured withoutintroducing crosstalk or errors on other qubits in the lattice. Adjacentpairs of qubits in the lattice can be addressed, for example, withtwo-qubit gate operations that are capable of generating entanglement,independent of other pairs in the lattice.

In some implementations, the quantum computing system 100 is constructedand operated according to a scalable quantum computing architecture. Forexample, in some cases, the architecture can be scaled to a large numberof qubits to achieve large-scale general purpose coherent quantumcomputing. In some instances, the architecture is adaptable and canincorporate a variety of modes for each technical component. Forexample, the architecture can be adapted to incorporate different typesof qubit devices, coupler devices, readout devices, signaling devices,etc. In some cases, the architecture of the quantum computing system 100provides a practicable and economical solution for large-scale quantumcomputation.

The example quantum processor cell 102 shown in FIG. 1 includes qubitsthat are used to store and process quantum information. In someinstances, all or part of the quantum processor cell 102 functions as aquantum processor, a quantum memory, or another type of subsystem. Thequantum processor cell 102 shown in FIG. 1 can be implemented, forexample, as the quantum processor cell 102A shown in FIG. 2, the quantumprocessor cell 102B shown in FIG. 9, or in another manner.

In the example quantum processor cell 102, the qubits each store asingle bit of quantum information, and the qubits can collectivelydefine the computational state of a quantum processor or quantum memory.The quantum processor cell 102 may also include readout devices thatselectively interact with the qubits to detect their quantum states. Forexample, the readout devices may generate readout signals that indicatethe computational state of the quantum processor or quantum memory. Thequantum processor cell 102 may also include couplers that selectivelyoperate on pairs of qubits and allow quantum interactions between thequbits. For example, the couplers may produce entanglement or othermulti-qubit states over two or more qubits in the quantum processor cell102.

In some implementations, the example quantum processor cell 102 canprocess the quantum information stored in the qubits by applying controlsignals to the qubits or to the couplers housed in the quantum processorcell. The control signals can be configured to encode information in thequbits, to process the information by performing logical gates or othertypes of operations, or to extract information from the qubits. In someexamples, the operations can be expressed as single-qubit gates,two-qubit gates, or other types of logical gates that operate on one ormore qubits. A sequence of operations can be applied to the qubits toperform a quantum algorithm. The quantum algorithm may correspond to acomputational task, a quantum error correction procedure, a quantumstate distillation procedure, or a combination of these and other typesof operations. The quantum processor cell 102 may output informationindicating the states of the qubits, for example, by applying controlsignals to the readout devices.

In the example shown in FIG. 1, the signal delivery system 106 providescommunication between the control system 110 and the quantum processorcell 102. For example, the signal delivery system 106 can receivecontrol signals (e.g., qubit control signals, readout control signals,coupler control signals, etc.) from the control system 110 and deliverthe control signals to the quantum processor cell 102. In someinstances, the signal delivery system 106 performs preprocessing, signalconditioning, or other operations to the control signals beforedelivering them to the quantum processor cell 102. In some instances,the signal delivery system 106 receives qubit readout signals from thequantum processor cell and delivers the qubit readout signals to thecontrol system 110. In some instances, the signal delivery system 106performs preprocessing, signal conditioning or other operations on thereadout signals before delivering them to the control system 110.

The signal delivery system 106 shown in FIG. 1 can be implementedaccording to the example signal delivery system 106A shown in FIG. 2,according to the example signal delivery system 106B shown in FIG. 17A,or in another manner. In some implementations, the signal deliverysystem 106 includes one or more input signal processing systems, one ormore output signal processing systems, or a combination of these andother types of components. Examples of features that may, in someimplementations, be included in a signal delivery system are shown anddescribed with respect to FIGS. 20A-20E, 23A-23B and others. Exampleoperations that may, in some implementations, be performed by a signaldelivery system are shown and described with respect to FIGS. 23A-23Band 24-28.

In the example quantum computing system 100 shown in FIG. 1, the controlsystem 110 controls operation of the quantum processor cell 102. Theexample control system 110 may include data processors, signalgenerators, interface components and other types of systems orsubsystems. In some cases, the control system 110 includes one or moreclassical computers or classical computing components. The examplecontrol system 110 shown in FIG. 1 can be implemented according to theexample control system 110A shown in FIG. 2, or the control system 110can be implemented in another manner. Examples of features that may, insome implementations, be included in a control system are shown in FIGS.23A-23B and 24-28. Example operations that may, in some implementations,be performed by a control system are shown in FIGS. 23A-23B and 24-28.

FIG. 2 is a schematic diagram of an example quantum computing system100A, showing example components and interactions of an example controlsystem 110A, an example signal delivery system 106A and an examplequantum processor cell (QPC) 102A. As shown in FIG. 2, the controlsystem 110A interfaces with the signal delivery system 106A throughcontrol system connector hardware 126; and the signal delivery system106A interfaces with the quantum processor cell 102A through QPC inputconnector hardware 136 and QPC output connector hardware 138. Theexample connector hardware elements 136, 138 shown in FIG. 2 can includesignal lines, processing components, feedthrough devices, or acombination of these and other types of components.

In the example shown in FIG. 2, the signal delivery system 106A and thequantum processor cell 102A are maintained in a QPC environment 101. TheQPC environment 101 can be provided, for example, by shieldingequipment, cryogenic equipment, and other types of environmental controlsystems. In some examples, the components in the QPC environment 101operate in a cryogenic temperature regime and are subject to very lowelectromagnetic and thermal noise. For example, magnetic shielding canbe used to shield the system components from stray magnetic fields,optical shielding can be used to shield the system components fromoptical noise, thermal shielding and cryogenic equipment can be used tomaintain the system components at controlled temperature, etc. Thelevels and types of noise that are tolerated or controlled in the QPCenvironment 101 can vary, for example, based on the features andoperational requirements of the quantum processor cell 102A and thesignal delivery system 106A.

The example control system 110A shown in FIG. 2 includes a signalgenerator system 120, a program interface 122 and a signal processorsystem 124. A control system may include additional or differentcomponents, and the components can operate as described with respect toFIG. 2 or in another manner. In some examples, components of the controlsystem 110A operate in a room temperature regime, an intermediatetemperature regime, or both. For example, the control system 110A can beconfigured to operate at much higher temperatures and be subject to muchhigher levels of noise than are present in the QPC environment 101. Inthe example shown, the control system connector hardware 126 can beconfigured to isolate the components in the QPC environment 101 fromnoise in the environment of the control system 110A.

The example signal generator system 120 generates control signals fromcontrol information provided by the program interface 122. For example,the signal generator system 120 may include a microwave signalgenerator, a DC control source, or other types of components thatgenerate control signals. In the example shown, the control signals canbe delivered to the quantum processor cell 102A by the signal deliverysystem 106A.

The example program interface 122 provides control information to thesignal generator system 120. For example, the program interface 122 caninclude a classical computing cluster, servers, databases, networks, orother types of classical computing equipment. In some instances, theprogram interface 122 includes one or more microprocessors runningsoftware, monitors or other display apparatus, interface devices, andother types of classical computing components. The program interface 122can generate control information, for example, based on a quantum taskor a quantum algorithm to be performed by the quantum computing system100A, based on qubit readout information, or based on a combination ofthese and other types of information.

The example signal processor system 124 can receive and process qubitreadout signals from the quantum processor cell 102A. For example, thesignal processor system 124 can include a digitizer, a microwave source,and other types of signal processing components. In the example shown,the qubit readout signals can be delivered to the signal processorsystem 124 by the signal delivery system 106A. The signal processorsystem 124 can process (e.g., digitize, or otherwise process) the qubitreadout signals and provide the processed information to the programinterface 122. The program interface 122 can extract qubit readout data,for example, to identify the quantum states of qubits in the quantumprocessor cell 102A.

The example signal delivery system 106A shown in FIG. 2 includes aninput signal processing system 128 and an output signal processingsystem 130. A signal delivery system may include additional or differentcomponents, and the components of a signal delivery system may operatein the manner shown in FIG. 2 or in another manner. In the example shownin FIG. 2, the signal generator system 120 communicates signals to theinput signal processing system 128 through the control system connectorhardware 126; and the output signal processing system 130 communicatessignals to the signal processor system 124 through the control systemconnector hardware 126.

The control system connector hardware 126 can include signal lines,signal processing hardware, filters, feedthrough devices (e.g.,light-tight feedthroughs, etc.), and other types of components. In someimplementations, the control system connector hardware 126 can spanmultiple different temperature and noise regimes. For example, thecontrol system connector hardware can include a series of temperaturestages (60 K, 3 K, 800 mK, 150 mK) that decrease between the highertemperature regime of the control system 110A and the lower temperatureregime of the QPC environment 101.

As shown in FIG. 2, the input signal processing system 128 includesinput processing hardware 132. An input signal processing system mayinclude various types of processing hardware, such as, for example,filters, attenuators, directional couplers, multiplexers, diplexers,bias components, signal channels, and other types of components. Anexample of an input signal processing system is shown in FIG. 20D; othertypes of input signal processing systems may be used.

In some examples, the input signal processing system 128 includesmultiple processing cards housed on a circuit board. The circuit boardcan include receptacle slots that form mechanical connections and signalpath connections between the circuit board and the processing cards. Thereceptacle slots can support the processing cards and allow theprocessing cards to be removed or exchanged for other components. Insome examples, the input signal processing system 128 includes multipleprocessing sections, and each processing section receives and processessignals for an operating domain that includes a group of devices in thequantum processor cell 102A. In some cases, each processing section ofthe input signal processing system 128 includes an input channel thatreceives multiplexed control signals, a de-multiplexer configured toseparate device control signals from the multiplexed control signal, andoutput channels configured to communicate the respective device controlsignals into the quantum processor cell 102A.

In some implementations, each multiplexed control signal received by theinput signal processing system 128 can include control signals formultiple devices in the quantum processor cell 102A. For example, insome cases, a multiplexed control signal includes qubit control signalsfor a group of the qubit devices, coupler control signals for a group ofthe coupler devices, or readout control signals for a group of thereadout devices. In some cases, the input signal processing system 128receives DC control signals, AC control signals, or combination of theseand other types of signals.

As shown in FIG. 2, the output signal processing system 130 includesoutput processing hardware 134. An output signal processing system mayinclude various types of processing hardware, such as, for example,isolators, superconducting amplifiers, semiconducting amplifiers,diplexers, multiplexers, power dividers, filters, signal channels, andother types of components. An example of an output signal processingsystem is shown in FIG. 20E; other types of output signal processingsystems may be used.

In some examples, the output signal processing system 130 includesmultiple processing cards housed on a circuit board. The circuit boardcan include receptacle slots that form mechanical connections and signalpath connections between the circuit board and the processing cards. Thereceptacle slots can support the processing cards and allow theprocessing cards to be removed or exchanged for other components. Insome examples, the output signal processing system includes multipleprocessing sections, and each processing section receives and processessignals from a group of devices in the quantum processor cell 102A. Insome cases, each processing section of the output signal processingsystem 130 includes input channels configured to receive the qubitreadout signals from a group of the readout devices in an operatingdomain, a multiplexer configured to generate a multiplexed readoutsignal from the qubit readout signals, and an output channel configuredto output the multiplexed readout signal.

The example quantum processor cell 102A shown in FIG. 2 includes anelectromagnetic waveguide system 104. In the example shown, theelectromagnetic waveguide system 104 houses a signal board 140, couplerdevices 142, qubit devices 144, and readout devices 146. A quantumprocessor cell may include additional or different components, and thecomponents of the quantum processor cell may operate as shown in FIG. 2or in another manner.

In the example shown in FIG. 2, the input signal processing system 128communicates signals to the signal board 140 through the QPC inputconnector hardware 136, and the signal board 140 communicates signals tothe output signal processing system 130 through the QPC output connectorhardware 138. The QPC input connector hardware 136 can be implemented,for example, as an input interconnect plate or another type ofstructure, and the QPC output connector hardware 138 can be implemented,for example, as an output interconnect plate or another type ofstructure. Example input and output interconnect plates are shown inFIGS. 20B-20C; other types of interconnect plates may be used.

In some examples, the QPC input connector hardware 136 includes one ormore input interconnect signal lines for each coupler device, each qubitdevice, and each readout device, and the QPC output connector hardware138 includes one or more output interconnect signal lines for eachreadout device. The interconnect signal lines can extend from anexterior of the electromagnetic waveguide system 104 to the interior ofthe electromagnetic waveguide system 104. In some cases, theinterconnect signal lines are supported by a plateau structure thatextends (e.g., in a vertical direction) between the signal board 140 andeither the input signal processing system 128 or the output signalprocessing system 130.

The example electromagnetic waveguide system 104 provides a low-noiseelectromagnetic environment for the qubit devices 144. Exampleattributes of electromagnetic waveguide systems are shown in FIGS.6A-6B, 7-8, 11A-11E, 13A-13F and others. In some examples, theelectromagnetic waveguide system 104 is formed by an assembly of quantumprocessor cell components. For example, the electromagnetic waveguidesystem 104 may be formed by assembling a lower member (a lid) to anupper member (a base) to form an enclosed (partially, substantially orfully enclosed) interior volume that corresponds to a lattice ofintersecting waveguides.

In some implementations, the example electromagnetic waveguide system104 provides an environment for a lattice of devices (e.g., qubit,coupler and readout devices). The environment provided by theelectromagnetic waveguide system 104 can meet or exceed the requisiteoperating conditions for each individual qubit, coupler and readoutdevice, and for quantum error correction on a large-scale lattice ofqubits. In some instances, the electromagnetic waveguide system 104includes apertures or other features that allow the delivery of signalsto the lattice of qubits and to the controllable coupling devices, andallow the extraction of readout signals from readout devices.

In some implementations, the example electromagnetic waveguide system104 suppresses signals (e.g., passively) to achieve low crosstalkbetween qubits, for example, such that signals applied to a targetdevice can be contained (e.g., localized in space) without significantleakage to non-target devices. In some cases, the exampleelectromagnetic waveguide system 104 provides shielding and isolation ofeach qubit from external noise and the external environment, and fromthe other qubits in the lattice. The electromagnetic environmentprovided by the electromagnetic waveguide system 104 can allow sustainedcoherence of individual qubits and entangled quantum states. Theelectromagnetic waveguide system 104 may allow neighboring qubits to becoupled to perform two-qubit gates, for example, when a coupler devicelocated between the neighboring qubits is selectively activated (e.g.,by control signals addressed to the coupler device).

In some implementations, the electromagnetic waveguide system 104 has aninterior surface that defines intersecting waveguides. An example of aninterior volume of intersecting waveguides formed by an electromagneticwaveguide system is shown in FIGS. 6A-6B, 7-8, 11B, 11E, 13F, 14A-14Band others. In some cases, intersecting waveguides include waveguidesections that meet at waveguide intersections. In the examples shown,the waveguide intersections include the portions of the interior volumethat are shared between the two or more intersecting waveguides. In someimplementations, the waveguide sections define cutoff frequencies, andeach waveguide section suppresses the propagation of electromagneticsignals below the cutoff frequency. Thus, electromagnetic signals belowthe cutoff frequency are evanesced (and not propagated) by the waveguidesections.

In some instances, the cutoff frequency for a waveguide section isdefined by the waveguide's cross-section. An electromagnetic waveguidesystem can include waveguide sections having square cross-sections,rectangular cross-sections, circular cross-sections, ellipticalcross-sections, irregular cross-sections, or cross-sections of othergeometries. Moreover, the cross-section of each waveguide section, takenperpendicular to the main axis of the waveguide (i.e., perpendicular tothe propagation axis), may vary along the main axis of the waveguide.Electromagnetic waves above the cutoff frequency are propagated in thedirection of the propagation axis, while electromagnetic waves below thecutoff frequency are evanesced (e.g., attenuated exponentially) in thedirection of the propagation axis. In some implementations, the largestdimension of the waveguide cross-sections is between 0.1 and 1.0centimeters. The largest dimension of a waveguide cross-section can be,for example, the height or width of a rectangular waveguidecross-section, the diameter of a circular waveguide cross-section, themajor axis of an elliptical waveguide cross-section, etc.

In some examples, the intersecting waveguides form a lattice, and thewaveguide intersections are arranged as a multi-dimensional array withinthe lattice. The lattice structure of the intersecting waveguides can bedefined by a first subset of waveguides extending in a first dimensionof the electromagnetic waveguide system (e.g., in the “x” direction of aCartesian coordinate system) and a second subset of the waveguidesextending in a second dimension of the electromagnetic waveguide system(e.g., in the “y” direction of a Cartesian coordinate system) to form atwo-dimensional array of waveguide intersections. In some cases, a thirdsubset of the waveguides extend in a third dimension of theelectromagnetic waveguide system (e.g., in the “z” direction of aCartesian coordinate system) to form a three-dimensional array ofwaveguide intersections. The intersecting waveguides may intersect atright angles, or they may intersect at non-right (acute or obtuse)angles. In some implementations, the distance between the waveguideintersections in a two-dimensional or three-dimensional array is in therange of 0.2 to 2.0 centimeters.

The devices within the electromagnetic waveguide system 104 can bearranged within the waveguide lattice, with the devices forming one ormore multi-dimensional device arrays within the electromagneticwaveguide system 104. For example, the qubit devices 144, the couplerdevices 142, the readout devices 146, or a subset or combination of themcan form a two-dimensional array or a three-dimensional array within theelectromagnetic waveguide system 104. A device array can be aligned withthe array of waveguide intersections, between the waveguideintersections, or a combination of these and other locations. Twoexamples of how qubit devices and coupler devices may be arranged in asystem of intersecting waveguides are shown in FIGS. 5A and 5B. Thedevices within the quantum processor cell 102A may be arranged inanother configuration.

In some implementations, the coupler devices 142 are housed betweenneighboring pairs of the qubit devices 144, and the readout devices 146are housed near the qubit devices 144. The qubit devices 144 can becontrolled individually, for example, by delivering qubit controlsignals to the individual qubit devices 144. The qubit devices 144 caninteract with each other, for example, through the coupler devices 142.The interactions between neighboring qubit devices 144 can becontrolled, for example, by delivering coupler control signals to theindividual coupler devices 142. The readout devices 146 can detect thestates of the qubit devices 144, for example, by interacting directlywith the respective qubit devices 144. The readout operations performedby the readout devices 146 can be controlled, for example, by deliveringreadout control signals to the individual readout devices 146.

The example signal board 140 can provide mechanical support for thecoupler devices 142, the qubit devices 144 and the readout devices 146.The interior surface of the electromagnetic waveguide system 104 mayalso provide direct or indirect mechanical support for the couplerdevices 142, the qubit devices 144 and the readout devices 146. Thesignal board 140 also includes signal lines that route control signalsand readout signals between the devices and the connector hardware. Inthe example shown in FIG. 2, the signal board 140 includes signal linesthat communicate qubit control signals from the QPC input connectorhardware 136 to the individual qubit devices 144, readout controlsignals from the QPC input connector hardware 136 to the individualreadout devices 146, and coupler control signals from the QPC inputconnector hardware 136 to the individual coupler devices 142. Theexample signal board 140 also includes signal lines that communicatequbit readout signals from the individual readout devices 146 to the QPCoutput connector hardware 138.

The example signal board 140 can include receptacles that hold therespective devices within the device array, and the signal board 140 caninclude arms that mechanically connect the receptacles to each other orto other portions of the signal board. Examples of features that may, insome implementations, be included in a signal board are shown in FIGS.10A-10B and others. The signal board 140 can be implemented, forexample, as a layered structure that includes multiple layers ofinsulating material and multiple layers of conducting or superconductingmaterial (or both). For example, the signal lines of the signal board140 can be formed by conductive strips between layers of insulatingmaterial in the signal board 140. The signal board 140 can include viasbetween conducting layers separated by insulating layers. The insulatingmaterials can include printed circuit boards materials or substrates(e.g., silicon, sapphire, fused quartz, diamond, beryllium oxide (BeO),aluminum nitride (AlN), or others).

In the example shown in FIG. 2, the qubit devices 144 can each be usedto encode and store a single bit of quantum information. Each of thequbit devices 144 has two eigenstates used as computational basis states(“0” and “1”), and each qubit device 144 can transition between itscomputational basis states or exist in an arbitrary superposition of itsbasis states. The quantum state of the qubit devices 144 can bemanipulated by qubit control signals provided by the signal deliverysystem 106A. An example of a qubit device is the transmon qubit shown inFIG. 3B. Other types of qubit devices may also be used.

In some examples, each qubit device has a fixed qubit operatingfrequency that is defined by an electronic circuit of the qubit device.For instance, a qubit device (e.g., a transmon qubit) may be implementedwithout a superconducting SQUID loop. In some examples, the operatingfrequency of a qubit device is tunable, for example, by application ofan offset field. For instance, a qubit device (e.g., a fluxonium qubit)may include a superconducting SQUID loop that is tunable by applicationof magnetic flux. A qubit device can be driven at its qubit operatingfrequency (or in some cases, at another frequency) to manipulate thequantum state of the qubit. For example, a single-qubit gate can beapplied to a qubit by applying a pulse that is configured to perform thesingle-qubit gate.

The readout devices 146 can be used to probe the quantum states of thequbit devices 144. The readout devices 146 can be operatively coupled toindividual qubit devices 144. In some examples, each readout device iscapacitively coupled to exactly one qubit device. The readout device canbe housed on a common chip or in a common structure with the associatedqubit device, or the readout device can be formed on a separate chip orin a separate structure from the qubit device.

In some examples, each readout device has a resonance that depends onthe quantum state of its associated qubit device. For example, theresonance frequency of a particular readout device can indicate thequantum state of the associated qubit device. The readout device can beprobed by a readout control signal, and the readout device can produce aqubit readout signal in response to the readout control signal. Theproperties of the qubit readout signal can indicate one of the twocomputational basis states of the associated qubit device. For instance,the readout device can produce a qubit readout signal by reflecting thereadout control signal with additional information. The additionalinformation can be, for example, a frequency shift, a phase shift, anamplitude shift, or a combination of these and other modifications, thatindicates the state of the associated qubit device.

In some implementations, solid state qubit devices can be realized fromindividual atoms or ions, individual electron or nuclear spins, charge-or spin-based quantum dots, superconducting quantum circuits based onJosephson junctions, impurities and defects in diamond or siliconcarbide, or other types of systems. Superconducting qubits withJosephson junctions can be embedded within a resonator for shielding andisolation and to provide a linear resonant mode coupled to the qubit forpurposes of qubit readout. The resonator may be formed from atwo-dimensional transmission line segment, for example, a coplanarwaveguide geometry, or a microstrip geometry. The resonator may beformed as a lumped or quasi-lumped element resonator, or the resonatormay be realized as a rectangular waveguide cavity, formed of a shorted(closed on both ends) section of a waveguide transmission line.

In some implementations, the example coupler devices 142 allow thequbits to be selectively coupled on-demand, to perform multi-qubitgates, to entangle neighboring pairs of qubits, or to perform othertypes of operations. The coupler devices 142 can have a high “on/off”ratio, which refers to the ratio of the coupling rate provided by thecoupler device when the coupler device is in its ON state versus its OFFstate. In some examples, the coupler devices 142 are implemented by aflux-based qubit, such as, for example, the fluxonium coupler shown inFIG. 3C. Other types of coupler devices may be used.

In some implementations, the coupling strength provided by each couplerdevice 142 can be tuned by coupler control signals communicated into thequantum processor cell. For instance, the coupling strength of anindividual coupler device 142 can decreased (e.g., to zero orsubstantially to zero) to place the coupler device in its OFF state, orthe coupling strength of an individual coupler device 142 can beincreased to place the coupler device in its ON state. Here, thecoupling strength between the qubit devices determines the rate ofcoupling between the qubit devices.

In some examples, the coupling strength of the electromagneticinteraction between qubit devices varies with an offset fieldexperienced by the coupling device that produces the electromagneticinteraction. For example, the coupler device may have a coupleroperating frequency that varies with the offset field experienced by thecoupling device, and the coupling operating frequency may influence thecoupling strength of the electromagnetic interaction between theneighboring pair of qubit devices. In such examples, the couplingstrength can be modified by tuning the coupler operating frequency. Insome examples, the coupler device may have another operating parameter(e.g., a capacitance or inductance) that varies with the offset fieldexperienced by the coupling device, and the operating parameter mayinfluence the coupling strength of the electromagnetic interactionbetween the neighboring pair of qubit devices. In such examples, thecoupling strength can be modified by tuning one or more of the relevantoperating parameter (e.g., the capacitance, inductance, etc.).

In some examples, each coupler device has a tunable coupler operatingfrequency. For example, the coupler operating frequency can be tuned byapplying an offset field to the coupler device. The offset field can be,for example, a magnetic bias field, a DC electrical voltage, or anothertype of constant field. To turn the coupler device “on,” the couplerdevice can be tuned to a particular coupler operating frequency anddriven at a drive frequency to increase the coupling rate between theneighboring pair of qubits. To turn the coupler device “off,” thecoupler device can be tuned to a different frequency that does notstrongly interact with the neighboring qubit devices.

As a particular example, a coupler device may include a superconductingquantum interference device (SQUID) loop whose resonance frequencydetermines the coupling strength of the electromagnetic interactionbetween the neighboring pair of qubit devices. For instance, thecoupling strength may be increased by setting the resonance frequency ofthe SQUID loop in a frequency range near the resonance frequency ofeither qubit device. In such examples, the resonance frequency of theSQUID loop can be tuned by controlling the amount of magnetic fluxexperienced by the SQUID loop. Thus, manipulating the magnetic flux canincrease or decrease the resonance frequency of the SQUID loop, which inturn influences the coupling strength provided by the coupler device. Inthis example, the magnetic flux through the SQUID loop is an offsetfield that can be modified in order to tune the coupler resonancefrequency. For instance, the coupler device can include an inductor thatis coupled to the SQUID loop by a mutual inductance. Thus, the magneticflux through the SQUID loop can be controlled by the DC component of thecurrent through the inductor. In some cases, the coupling strength iscontrolled by both AC and DC components of the coupler control signal.

In some implementations, coupler devices that are tunable by applicationof an offset field are used with qubit devices that do not respond tooffset fields. This may allow the coupler devices to be selectivelyactivated by an offset field that does not disturb the informationencoded in the qubit device. For instance, although the offset field maycause the coupler device to produce an electromagnetic interactionbetween neighboring qubit devices, the offset field does not directlyinteract with the qubit device or disturb the quantum state of the qubitdevice even if the qubit device experiences the offset field. Thus, thecombination of tunable couplers with fixed-frequency qubit devices mayallow selective, on-demand coupling of qubit devices while improvingperformance of the qubit devices. For example, the fixed-frequency qubitdevices may have longer coherence times, may be more robust againstenvironmental or applied offset fields, etc.

In some instances, information is encoded in the qubit devices 144, andthe information can be processed by operation of the qubit devices andthe coupler devices. For instance, input information can be encoded inthe computational states or computational subspaces defined by some ofall of the qubit devices 144. The information can be processed, forexample, by applying a quantum algorithm or other operations to theinput information. The quantum algorithm may be decomposed as gates orinstruction sets that are performed by the qubit devices and couplerdevices over a series of clock cycles. For instance, a quantum algorithmmay be executed by a combination of single-qubit gates and two-qubitgates. In some cases, information is processed in another manner.Processing the information encoded in the qubit devices produces outputinformation that can be extracted from the qubit devices. The outputinformation can be extracted, for example, by performing statetomography or individual readout operations. In some instances, theoutput information is extracted over multiple clock cycles or inparallel with the processing operations.

In some instances, the quantum computing system 100A operates based on aclock cycle or another type of synchronization scheme. For example, aquantum algorithm or quantum computing task may be expressed as asequence of instructions corresponding to quantum gates, readouts, orother operations on the qubit devices 144, and a subset of theinstructions can be executed on each clock cycle. In some instances, oneach clock cycle, the control system 110A generates control signals toimplement a subset of instructions, control signals are delivered to thequantum processor cell 102A, and qubit readout signals are delivered tothe control system 110A. The control signals delivered on each clockcycle can be configured, for example, based on the sequence ofinstructions, based on readout signals from a previous cycle, quantumerror correction operations, error matching calculations, otherinformation, or a combination of these.

Various implementations of the quantum computing system 100A aredescribed below, including various alternatives for its subsystems andtheir respective components along with various methods for operating thequantum computing system 100A and its subsystems.

FIGS. 3A-3E show aspects of example devices in a device array 148 thatmay be housed in a quantum processor cell and used to perform quantumoperations. Here, the device array 148 includes a subset of the qubitdevices 144, their corresponding readout devices 146 and a subset of thecoupler devices 142 that may be housed in the example quantum processorcell 102A. FIG. 3A shows an equivalent circuit for a portion of thedevice array 148 that includes qubit devices 144-j and 144-(j+1),corresponding readout devices 146-j and 146-(j+1), and a tunable couplerdevice 142-(j,j+1) disposed between the qubit devices 144-j and144-(j+1). In some cases, the quantum processor cell 102A may beimplemented using other types of qubit devices, readout devices andcoupler devices. In the examples shown in FIGS. 3A-3E, both of the qubitdevices 144-j and 144-(j+1) are capacitively coupled to the couplerdevice 142-(j,j+1) by respective differential capacitances 150-j and150-(j+1). Also, each of the qubit devices 144-j and 144-(j+1) iscapacitively coupled to its respective readout device 146-j and146-(j,j+1) by respective differential capacitances 152-j and 152-(j+1).The qubit devices and coupler devices may be implemented by other typesof systems, and the features and components represented in FIG. 3A canbe extended in a larger two-dimensional or three-dimensional array ofdevices.

Write signals (e.g., coupler control signals, qubit control signals,readout control signals, etc.) can be transmitted from the input signalprocessing system 128, through the signal board 140, to various inputports of the device array 148. In some implementations, the same portcan be used for both write signals (received by a device) and readoutsignals (reflected by a device). The example shown in FIG. 3A can beadapted to include input ports that are distinct from the output ports.For instance, the readout resonators can be connected in transmissioninstead of reflection (as shown in FIG. 3A), and the input ports (thatreceive readout control signals from the input signal processing system)can be distinct from the output ports (that send qubit readout signalsto the output signal processing system).

An example input port is shown in FIG. 3A as a coupler control inputport 154-(j,j+1). In this manner, the tunable coupler device 142-(j,j+1)is inductively coupled, at the coupler control input port 154-(j,j+1),to a source of coupler control signals. Other examples of input portsare shown in FIG. 3A as the qubit+readout control port 156-j and thequbit+readout control port 156-(j+1). In this manner, each of thereadout devices 146-j and 146-j+1 is capacitively coupled, by therespective qubit+readout control ports 156-j and 156-(j+1), to a sourceof qubit control signals and a source of readout control signals.Additionally, readout signals (e.g., qubit readout signals) are receivedby the output signal processing system 130, through the signal board140, from various output ports in the device array 148. In the exampledevice array 148 shown in FIG. 3A, the qubit+readout control ports 156-jand 156-(j+1) may operate as output ports. Other types of input andoutput ports may be used.

In the example shown in FIG. 3A, each of the qubit devices 144-j,144-(j+1) includes a Josephson junction (represented by the symbol “X”in FIG. 3A) and a shunt capacitance. FIG. 3B shows an exampleimplementation of a qubit device 144 as a transmon qubit 158. FIG. 3Dshows an equivalent circuit 302 for the example transmon device shown inFIG. 3B. The transmon qubit 158 is an example of a charge qubit andincludes a substrate 162 (e.g., formed from sapphire, silicon, etc.)that supports a superconducting thin film 164 (e.g., formed fromaluminum, niobium, etc.). The example transmon qubit 158 shown in FIG.3B includes a Josephson junction 160A and a shunt capacitance. In thisexample, the shunt capacitance is formed in a topologically closedmanner to reduce far-field coupling and spurious qubit couplings tonon-adjacent couplers and non-neighboring qubits. A differentialcapacitance of the inner electrode 166 and the outer electrode 168 ofthe example transmon qubit 158 to an electrode of an adjacent device(e.g., a coupler device, a readout device, or a qubit+readout controlport) forms an effective input capacitance 150 or 152 for capacitivelycoupling the transmon qubit 158 to the adjacent device or to an inputport or to an output port. In other implementations of the device array148, the qubit devices 144-j, 144-(j+1) can be configured as flux qubits(e.g., as fluxonium qubits) or another type of qubit device. In somecases, the transmon qubit 158 can be fabricated, for example, bydouble-angle evaporation of thin-film aluminum onto a sapphire orsilicon substrate, or by another fabrication process.

As shown in the equivalent circuit 302 in FIG. 3D, the transmon deviceincludes a Josephson junction 310 and a shunt capacitance 314. The shuntcapacitance 314 can be formed in a topologically closed manner, forinstance, to reduce far-field coupling and spurious qubit couplings tonon-adjacent couplers and non-neighboring qubits. The effective inputcapacitance 312 can be formed by a differential capacitance of the innerelectrode 166 and the outer electrode 168 of the transmon to a nearbyelectrode, which may be a control electrode or a coupling electrode.

In the example shown in FIG. 3A, the coupler circuitry of the tunablecoupler device 142-(j,j+1) includes a Josephson junction (represented bythe symbol “X” in FIG. 3A), a shunt inductance and a shunt capacitance.The tunable coupler device 142-(j,j+1) also includes bias circuitry(connected to the coupler control input port 154-(j,j+1)) that isconfigured to apply an offset field to the coupler circuitry. Inparticular, the bias circuitry includes an inductor that has a mutualinductance with the coupler circuitry. In the example shown, themagnetic flux generated by the bias circuitry controls a resonancefrequency of the coupler circuitry of the tunable coupler device142-(j,j+1).

In the example shown in FIG. 3A, the resonance frequency of the couplercircuitry in the coupler device 142-(j,j+1) determines the couplingstrength of the electromagnetic interaction between the neighboring pairof qubit devices 144-j and 144-(j+1). For instance, the couplingstrength may be increased by setting the resonance frequency of thecoupler circuitry in a frequency range near the resonance frequency ofeither qubit device 144-j, 144-(j+1). The resonance frequency of thecoupler circuitry can be tuned by controlling the amount of magneticflux experienced by the coupler circuitry. Thus, manipulating themagnetic flux can increase or decrease the resonance frequency of thecoupler circuitry, which in turn influences the coupling strengthprovided by the coupler device 142-(j,j+1). In this example, themagnetic flux through coupler circuitry is an offset field that can bemodified in order to tune the coupler resonance frequency. Because theinductor in the bias circuitry has a mutual inductance with the couplercircuitry, the magnetic flux through the coupler circuitry can becontrolled by the DC component of the current through the inductor. Insome instances, the coupling strength is controlled by both the AC andDC components received through the coupler control input port154-(j,j+1).

FIG. 3C shows an implementation of a coupler device 142 as a fluxoniumcoupler 170. FIG. 3E shows an equivalent circuit 304 for the examplefluxonium device shown in FIG. 3C. The example fluxonium coupler 170shown in FIG. 3C includes a substrate 172 (e.g., formed from silicon,sapphire, etc.) that supports a superconducting thin film 174 (e.g.,formed from aluminum, niobium, etc.). The example fluxonium coupler 170includes a Josephson junction 160B, a shunt inductance and a shuntcapacitance connected in parallel and forming a loop 176. A magneticflux signal 178 can be applied to the loop 176. A differentialcapacitance 150 across the Josephson junction 160B may be formed of atopologically closed capacitance where an inner island 180 is encircledby an outer island 182. The differential capacitance 150 can provide acharge-coupling control port to an adjacent qubit device 144. In otherimplementations of the device array 148, a coupler device can beconfigured as a charge qubit (e.g., as a transmon qubit), a parametricfrequency converter controlled by one or more microwave pump signals, oranother type of device. In some cases, the fluxonium coupler 170 can befabricated, for example, by double-angle evaporation of thin-filmaluminum onto a sapphire substrate, or by another fabrication process.

As shown in the equivalent circuit 304 in FIG. 3E, the fluxonium deviceincludes a Josephson junction 320, a shunt inductance 324 and a shuntcapacitance 328 connected in a loop to which a magnetic flux signal 326can be applied. The magnetic flux signal 326 can be applied to the loop,for example, by applying a DC signal to bias circuitry that has a mutualinductance with the loop. The input capacitance 322 across the Josephsonjunction 320 can provide a charge-coupling control port. Thecharge-coupling control port may be formed of a topologically closedcapacitance, for instance, where the inner island 180 is encircled bythe outer island 182. In some implementations, a control or couplingport can be realized by coupling the device with a differentialcapacitance with respect to these two islands to a nearby electrode.

Various example techniques for operating devices of the device array 148to encode information in the qubit devices, to implement one-qubit gateoperations or multi-qubit gate operations, or to perform otheroperations based on instructions received from control system 110A, aredescribed below.

FIG. 4A is an example energy level diagram 161 that shows aspects ofoperating a qubit device 144-j using an example qubit control signal 163(also referred to as a write signal). In some implementations, othertypes of qubit control signals (e.g., signals at other frequencies,etc.) can be used to operate the qubit device 144-j. In some instances,the qubit control signal 163 can be applied to the qubit+readout controlport 156-j of the example device array 148 shown in FIG. 3A, forexample, to manipulate a quantum state of the qubit device 144-j. Theexample qubit device 144-j has a fixed qubit operating frequency fq-jthat is defined by an electronic circuit of the qubit device (e.g.,electronic circuits of qubit devices shown in FIGS. 3A-3E). The qubitoperating frequency fq-j is independent of an offset electromagneticfield (e.g., applied or environmental magnetic flux, or applied orenvironmental current or voltage) experienced by the qubit device 144-j.The example qubit device 144-j has two computational basis states (“0”and “1”). The qubit device can exist in either of its computationalbasis states or any arbitrary superposition of its basis states. Afrequency of the example qubit control signal 163 is set to the qubitoperating frequency fq-j, such that the qubit control signal 163 causestransitions between the computational basis states of the qubit device144-j. In some instances, the qubit control signal 163 is configured toperform a particular single-qubit gate, to encode input information, orto execute another operation by manipulating an amplitude or phase (orboth) of the qubit control signal 163.

FIG. 4B shows an example frequency diagram 165 for the example readoutdevice 146-j associated with a qubit device 144-j. In some instances, areadout control signal 167 (also referred to as a read signal) can beapplied to the qubit+readout control port 156-j of the device array 148shown in FIG. 3A. The readout device 146-j has a resonant circuit tunedto a resonant frequency fr that is different from the qubit operatingfrequency fq−j of the qubit device 144-j to which it is associated. Insome implementations, the qubit operating frequency can be less than thereadout frequency (fq−j<fr). In some implementations, the qubitoperating frequency can be greater than the readout frequency (fq−j>fr).When the frequency of the readout control signal 167 is set to theresonant frequency fr, which is different from qubit operating frequencyfq−j, the readout control signal 167 probes a state of the qubit device144-j, which can project the state of the qubit onto one of its twocomputational basis states.

In some examples, the qubit readout signal 169 produced by the readoutdevice is a frequency-shifted instance of the readout control signal167, and the frequency-shifted signal is reflected by the resonantcircuit of the readout device 146-j. For instance, the readout device146-j can produce the qubit readout signal 169 by reflecting the readoutcontrol signal 167 with a frequency shift of ±δf. In the example shown,a frequency shift of +δf indicates that the qubit device is in the “0”computational basis state, and a frequency shift of −δf indicate thatthe qubit device is in the “1” computational basis state. In someexamples, the qubit readout signal 169 produced by the readout device isa phase-shifted instance of the readout control signal 167. Forinstance, the readout device 146-j can produce the qubit readout signal169 by reflecting the readout control signal 167 with a phase shift of±δϕ, where a phase shift of +δϕ indicates that the qubit device is inthe “0” computational basis state, and a frequency shift of −δϕ indicatethat the qubit device is in the “1” computational basis state.

In some implementations, the qubit readout signal 169 is reflected backout the same qubit+readout control port 156-j. In other implementations,the qubit readout signal 169 is redirected to a different, output portof the readout device 146-j. In this manner, characteristics of thequbit readout signal 169 measured at the qubit+readout control port156-j or at another output port can be used to determine the state ofthe qubit device 144-j. For example, measurements of a magnitude and aphase shift of the qubit readout signal 169 relative to the readoutcontrol signal 167 can indicate of a state of the qubit device 144-j. Insome instances, measurements of a change in amplitude or a change inphase of the qubit readout signal 169 relative to the readout controlsignal 167 indicate the state of the qubit device 144-j.

FIGS. 4C-4D show aspects of operating an example tunable coupler device142-(j,j+1) to couple adjacent qubit devices 144-j and 144-(j+1). Here,the qubit operating frequencies fq−j, fq−(j+1) of the adjacent qubitdevices 144-j and 144-(j+1) are different from each other. As describedabove, each of the qubit devices 144-j and 144-(j+1) has twocomputational basis states (“0” and “1”). The tunable coupler device142-(j,j+1) disposed between the qubit devices 144-j and 144-(j+1) isconfigured to generate an electromagnetic interaction between the qubitdevices 144-j and 144-(j+1). In this manner, the tunable coupler device142-(j,j+1) allows the qubit devices 144-j and 144-(j+1) to beselectively coupled on-demand, to perform multi-qubit gates, to entanglethe pair of qubit devices 144-j and 144-(j+1), or to perform other typesof operations. Here, the tunable coupler device 142-(j,j+1) has a high“on/off” ratio, which refers to the ratio of the coupling rate providedby the tunable coupler device 142-(j,j+1) when the coupler device is inits ON state versus its OFF state.

FIG. 4C shows an example energy level diagram 184 for an example couplerdevice in its OFF state, and FIG. 4D shows an example energy leveldiagram for the example coupler device in its ON state. FIG. 4E shows anexample coupler control signal 188 that can control operation of theexample coupler device. A coupler device may have other features orattributes, and may operate in another manner.

The example energy level diagram 184 shown in FIG. 4C represents aportion of the device array 148 when the tunable coupler device142-(j,j+1) is tuned to its OFF state. In its OFF state, the tunablecoupler device 142-(j,j+1) is operated at a frequency (fc-off) that ishigher than either of the qubit operating frequencies fq−j, fq−(j+1).With the coupler device 142-(j,j+1) in its OFF state, the couplingstrength (and therefore, the rate of coupling) between the adjacentqubit devices 144-j and 144-(j+1) is low because of the mismatch betweenfc-off and either of the qubit operating frequencies fq−j, fq−(j+1). Forexample, when the coupler device 142-(j,j+1) is in the OFF state, thecoupling between the adjacent qubit devices 144-j and 144-(j+1) can be asecond- or third-order interaction. Thus, the example tunable couplerdevice 142-(j,j+1) is said to be in its OFF state when operated atfc-off.

The example energy level diagram 186 shown in FIG. 4D represents thesame portion of the device array 148 when the tunable coupler device142-(j,j+1) is tuned to its ON state. In its ON state, the tunablecoupler device 142-(j,j+1) is operated at a frequency fc-on that istuned near one of the qubit operating frequencies fq−j or fq−(j+1). Withthe coupler device 142-(j,j+1) in its ON state, the coupling strength(and therefore, the rate of coupling) between the adjacent qubit devices144-j and 144-(j+1) is high because fc-on matches or is tuned near oneof the qubit operating frequencies fq−j or fq−(j+1). For example, whenthe coupler device 142-(j,j+1) is in the ON state, the coupling betweenthe adjacent qubit devices 144-j and 144-(j+1) can be a first-orderinteraction. Thus, the example tunable coupler device 142-(j,j+1) issaid to be in its ON state when operated at fc-on.

FIG. 4E shows time dependence of an example coupler control signal 188that can be used to operate the tunable coupler device 142-(j,j+1). Insome instances, the coupler control signal 188 can be applied to thecoupler control input port 154-(j,j+1) of the example device array 148shown in FIG. 3A. As shown in FIG. 4E, before a time T1, the tunablecoupler device 142-(j,j+1) is operated at the operational frequencyfc-off and, hence, it is in its OFF state. When the tunable couplerdevice 142-(j,j+1) is in its OFF state, the coupling rate of theadjacent qubit devices 144-j and 144-(j+1) is low due to the lowcoupling strength. For instance, in some examples, the coupling rate canbe in the range of approximately 50 kHz or less. As shown in FIG. 4E, attime T1 a bias (or offset) component of the coupler control signal 188is applied at the coupler control input port 154-(j,j+1), which causesthe tunable coupler device 142-(j,j+1) to transition into its ON state.The bias component can be, for example, a bias current that creates amagnetic bias field (e.g., flux 178 through the loop 176 shown in FIG.3C). From the time T1 to a later time T4, the tunable coupler device142-(j,j+1) is operated at operational frequency fc-on and, hence, it isin its ON state. When the tunable coupler device 142-(j,j+1) is in itsON state, the coupling rate for the adjacent qubit devices 144-j and144-(j+1) is higher due to the higher coupling strength. For instance,in some examples, the coupling rate can be in the range of approximately200 kHz to 2 MHz or more. At an intermediate time T2 (where T1<T2<T4) anAC (alternating current) component of the coupler control signal 188 issuperposed with the bias component, at the coupler control input port154-(j,j+1), to increase the rate of coupling between the adjacent qubitdevices 144-j and 144-(j+1). Here, the AC component of the couplercontrol signal 188 is a radio frequency (RF) or microwave frequencycurrent, and the AC component is maintained until an intermediate timeT3 (where T2<T3<T4), forming a pulse of duration T3−T2. In someinstances, the frequency of the pulse can be at or near either a sum ofthe neighboring qubit operating frequencies (i.e., (fq−j)+(fq−(j+1))) ora difference of the neighboring qubit operating frequencies (i.e.,(fq−j)−(fq−(j+1)). In this manner, a high rate of coupling between theadjacent qubit devices 144-j and 144-(j+1) can be maintained over theduration (T3−T2) of the AC component. For instance, in some examples,the coupling rate can be in the range of approximately 5 MHz to 500 MHz.At time T3, the AC component of the coupler control signal 188 isremoved, which reduces the coupling strength between the adjacent qubitdevices 144-j and 144-(j+1). Between time T3 and time T4, the couplercontrol signal 188 continues to have the bias component, so the tunablecoupler device 142-(j,j+1) remains in its ON state. At T4, the biascomponent of the coupler control signal 188 is removed, which causes thetunable coupler device 142-(j,j+1) to return to its OFF state. After T4,the tunable coupler device 142-(j,j+1) is operated at operationalfrequency fc-off and, hence, remains in its OFF state.

All or part of the portion of the example device array 148 illustratedin FIG. 3A can be copied multiple times, as a unit cell, to extend thedevice array 148 along a path (e.g., along x-axis of a Cartesiancoordinate system), on a surface (e.g., x-y plane of a Cartesiancoordinate system) or in space (e.g., as layers parallel to x-y planethat are distributed along a z-axis of a Cartesian coordinate system).For example, fault-tolerant quantum computing can be achieved byimplementing gate-based models in a two-dimensional (2D) device array148A that includes a large number of nearest-neighbor-coupled qubitdevices 144. In some cases, a 2D device array 148A can allow each qubitdevice 144 to be independently controlled and measured withoutintroducing crosstalk or errors on other qubit devices 144 in the 2Ddevice array 148A. In some instances, nearest-neighbor pairs of qubitdevices 144 in the 2D device array 148A can be addressable withtwo-qubit gate operations capable of generating entanglement,independent of all other such pairs in the 2D device array 148A. Asanother example, fault-tolerant quantum computing can likewise beperformed, and possibly advantaged, in a three-dimensional (3D) devicearray 148B (e.g., as shown in FIGS. 14A and 15) that includes a largenumber of nearest-neighbor-coupled qubit devices 144.

In some implementations, to carry out large-scale, fault tolerantquantum computing, at least some of the following technical features canbe provided in the example device arrays described here. One suchfeature is the delivery of control signals to qubit devices 144 andtunable coupling devices 142 of a 2D device array 148A or a 3D devicearray 148B, and another such feature is the extraction of measurementsignals from the qubit devices 144 being performed with low-crosstalk ofthe applied signals from target qubit devices to non-target qubitdevices. Another such feature is the shielding and isolation of thequbit device 144-j from external noise, from the external environment,and from each other qubit device 144-(j+k) in the 2D device array 148Aor the 3D device array 148B to which the qubit device 144-j is notspecifically coupled (k≠0 or ±1) for performing a two-qubit gate. Yetanother such feature is the ability to sustain coherence of individualand entangled quantum states of the qubit devices 144 of the 2D devicearray 148A or the 3D device array 148B.

In some instances, to achieve one or more of the above-noted features orother advantages, the 2D device array 148A or the 3D device array 148Bcan be embedded in an electromagnetic waveguide system 104 that includesa lattice of intersecting waveguides. Here, the lattice of intersectingwaveguides is geometrically commensurate with the 2D device array 148Aor the 3D device array 148B. Moreover, the intersecting waveguides areconfigured such that electromagnetic modes of the waveguides areevanescent with respect to relevant operating frequencies fq−j of thequbit devices 144-j and fc-on/fc-off of adjacent tunable coupler devices142-(j,j±1) that control their respective coupling with nearest-neighborqubit devices 144-(j±1). In this manner, the lattice of intersectingwaveguides can provide high (e.g., exponential) electromagneticisolation between nearest-neighbor array sites (j,j+1). Moreover,individual qubit devices 144 in the 2D device array 148A or the 3Ddevice array 148B can be shielded and isolated from all but theirnearest-neighbors, and all qubit devices 144 can be isolated from theexternal electromagnetic environment. Additionally, apertures formed inthe walls of the lattice of intersecting waveguides can provide ports toinject or extract (or both) electromagnetic signals for control ormeasurement (or both).

Multiple example arrangements of the 2D device array 148A or the 3Ddevice array 148B within an electromagnetic waveguide system 104 thatincludes a lattice of intersecting waveguides are described below.

FIGS. 5A and 5B are schematic diagrams of example systems 200A and200A′, respectively, each of which includes an electromagnetic waveguidesystem 104A that defines a 2D lattice of intersecting waveguides. Here,a subset of the waveguides in the 2D lattice (e.g., the waveguidesoriented along the x-axis of a Cartesian coordinate system) intersectanother subset of the waveguides in the 2D lattice (e.g., the waveguidesoriented along the y-axis of the Cartesian coordinate system) atintersections 202 (also referred to as nodes). Moreover, the waveguidesform intervals (also referred to as bonds) 204 between the intersections202.

In the example illustrated in FIG. 5A, the system 200A includes a devicearray 148A arranged within the 2D lattice of intersecting waveguidesdefined by the electromagnetic waveguide system 104A. The device array148A is an example of a 2D device array, where qubit devices 144A areplaced at nodes of the device array 148A and coupler devices 142A areplaced along the bonds (between the nodes) of the device array 148A. Inthis manner, the device array 148A forms rows of devices (e.g., alongthe x-axis of a Cartesian coordinate system) and columns of devices(e.g., along the y-axis of a Cartesian coordinate system). The devicearray 148A also is referred to as the 2D device array 148A. Each qubitdevice 144A of the example 2D device array 148A has four adjacentcoupler devices 142A and four nearest-neighbor qubit devices 144A.Moreover, each of the coupler devices 142A of the example 2D devicearray 148A has two adjacent qubit devices 144A.

In the example shown in FIG. 5A, the bonds of the 2D device array 148Ahave the same size and orientation as the intervals 204 of the 2Dlattice of intersecting waveguides; thus, the 2D device array 148A iscommensurate to the 2D lattice of intersecting waveguides. Here, theexample 2D device array 148A is aligned with the 2D lattice ofintersecting waveguides such that the nodes of the 2D device array 148Acoincide with the intersections 202 of the 2D lattice of intersectingwaveguides. In this manner, qubit devices 144A of the 2D device array148A are placed inside the electromagnetic waveguide system 104A atintersections 202 of the 2D lattice of intersecting waveguides, andcoupler devices 142A of the 2D device array 148A are placed inside theelectromagnetic waveguide system 104A along intervals 204 (betweenintersections 202) of the 2D lattice of intersecting waveguides. In someimplementations, the distance between each adjacent pair of qubitdevices 144A in the 2D device array 148A is in the range of 0.2 to 2.0centimeters. In the example device array 148A shown in FIG. 5A, eachcoupler device 142A is operably coupled between a single pair ofneighboring qubit devices 144A, and each neighboring pair of qubitdevices 144A is operably coupled by a single coupler device 142A.

In the example illustrated in FIG. 5B, the system 200A′ includes adevice array 148A′ arranged within the 2D lattice of intersectingwaveguides of the electromagnetic waveguide system 104A. The exampledevice array 148A′ is an example of a 2D device array, where couplerdevices 142B are placed at nodes of the device array 148A′ and qubitdevices 144B are placed along bonds (between the nodes) of the devicearray 148A′. In this manner, the device array 148A′ forms rows ofdevices (e.g., along the x-axis of a Cartesian coordinate system) andcolumns of devices (e.g., along the y-axis of a Cartesian coordinatesystem). The device array 148A′ is also referred to as the 2D devicearray 148A′. Each coupler device 142B of the example 2D device array148A′ has four adjacent qubit devices 144B. Moreover, each qubit device144B of the example 2D device array 148A′ has two adjacent couplerdevices 142B, and six other qubit devices 144B are also adjacent to thetwo adjacent coupler devices 142B.

In the example shown in FIG. 5B, the bonds of the 2D device array 148A′have the same size and orientation as the intervals 204 of the 2Dlattice of intersecting waveguides; thus, the 2D device array 148A′ iscommensurate to the 2D lattice of intersecting waveguides. Here, the 2Ddevice array 148A′ is aligned with the 2D lattice of intersectingwaveguides such that the nodes of the 2D device array 148A′ coincidewith the intersections 202 of the 2D lattice of intersecting waveguides.In this manner, coupler devices 142B of the 2D device array 148A′ areplaced inside the electromagnetic waveguide system 104A at intersections202 of the 2D lattice of intersecting waveguides, and qubit devices 144Bof the 2D device array 148A′ are placed inside the electromagneticwaveguide system 104A along intervals 204 (between intersections 202) ofthe 2D lattice of intersecting waveguides. In some implementations, thedistance between each adjacent pair of coupler devices 142B in the 2Ddevice array 148A′ is in the range of 0.2 to 2.0 centimeters. In theexample device array 148A shown in FIG. 5A, each coupler device 142A isoperably coupled between a single pair of neighboring qubit devices144A, and each neighboring pair of qubit devices 144A is operablycoupled by a single coupler device 142A.

In some implementations, the arrangement of the devices in the devicearray corresponds to a multi-dimensional device lattice, where thedevice lattice includes unit cells extending along each dimension. Forinstance, the devices shown in FIGS. 5A and 5B are arranged as atwo-dimensional device lattice, where each unit cell of the devicelattice includes one or more qubit devices and one or more couplerdevices. In some cases, each unit cell of the device lattice can includeone or more readout devices. Each unit cell in a two-dimensional devicearray can include one or more rows and one or more columns of devices.

In some cases, two-dimensional lattices (e.g., either of those shown inFIG. 5A or 5B, or others) can be extended into three dimensions. Forinstance, the lattice that forms the example device array 148A can beextend to three dimensions by forming layers of the example device array148A, with additional coupler devices between the nearest neighbor qubitdevices of adjacent layers; or the example device array 148A′ can beextend to three dimensions by forming layers of the example device array148A′ with additional qubit devices between the nearest neighbor couplerdevices of adjacent layers. Each unit cell in a three-dimensional devicearray can include one or more rows, one or more columns, and one or morelayers of devices.

In some implementations, the device lattice can be aligned in amulti-dimensional waveguide lattice formed by intersecting waveguidesections. For instance, each unit cell of the device lattice can behoused in section of the electromagnetic waveguide system thatcorresponds to one or more unit cells of the waveguide lattice.

FIG. 6A shows a portion of the interior volume 206 of an exampleelectromagnetic waveguide system 104A. In particular, FIG. 6A shows aportion of the electromagnetic waveguide system 104A where twowaveguides intersect at a waveguide intersection 202. In the exampleshown, a first of the two waveguides includes two intervals 204-xoriented along the x-axis, and a second of the two waveguides includestwo intervals 204-y oriented along the y-axis. In some instances, aqubit device 144A of the 2D device array 148A or a coupler device 142Bof the 2D device array 148A′ can be placed at the example waveguideintersection 202.

FIG. 6B shows a close-up view of an example interval 204 of a waveguide.In this example, the waveguide interval 204 is formed by a base 208, twoopposing side walls 210 and a lid 212. As shown in FIG. 6B, the base 208has an upper surface that is parallel to the x-y plane and defines alower boundary of a portion of the interior volume 206. As shown in FIG.6B, the two side walls 210 include vertical side surfaces that areorthogonal to the base 208 and parallel to each other, and the sidewalls 210 define side boundaries of a portion of the interior volume206. As shown in FIG. 6B, the lid 212 has a lower surface that isparallel to and opposes the upper surface of the base 208; the lowersurface of the lid 212 defines an upper boundary of a portion of theinterior volume 206. In this manner, the base 208, the side walls 210and the lid 212 partially enclose the interior volume 206 and define across section of the example interval 204. In the example shown, thecross-section of each waveguide interval 204 is at least partiallydefined by opposing pairs of right and left side walls (provided by theside walls 210), and opposing pairs of upper and lower side walls(provided by the upper surface of the base 208 and the lower surface ofthe lid 212). At each waveguide intersection 202, the right and leftsidewalls of the waveguide that extends along the x-axis meets the rightand left sidewalls of the waveguide that extends along the y-axis. Thebase 208, the side walls 210 and the lid 212 can be formed from aconductor material, a superconductor material or a combination thereof.

The base 208, the side walls 210 and the lid 212 can be formed in anumber of different ways, for example, as an assembly of multiplecomponents or as an integrated structure. In some implementations, thebase 208, the side walls 210 and the lid 212 can be formed as amicro-machined silicon wafer device, for example, from one or morewafers etched and coated with thin film superconductor material such asaluminum or niobium. In some implementations, the base 208, the sidewalls 210 and the lid 212 can be formed from bulk superconducting metalmachined to form the base, lid, and sidewalls of the electromagneticwaveguide system. In some implementations, the base 208 and the sidewalls 210 can be formed as a single component that is then assembled toanother component that includes the lid 212; or the lid 212 and the sidewalls 210 can be formed as a single component that is then assembled toanother component that includes the base 208; or the base 208, the sidewalls 210, and the lid 212 can be formed as a layered or laminatedstructure.

One or more of the base 208, the side walls 210 or the lid 212 caninclude an aperture from the interior volume 206. In some cases, theapertures are openings through the interior surface that defines theinterior volume 206. In some examples, apertures are located adjacent tothe regions where qubit devices or coupler devices reside. In theexample illustrated in FIG. 6B, an aperture 214 is provided through thelid 212 that defines the example interval 204. Apertures mayadditionally or alternatively be provided in the base 208 or side walls210.

In some instances, control signals can be transmitted, through theaperture 214, from a signal source located outside the electromagneticwaveguide system 104A to a qubit device 144A/144B or a coupler device142A/142B located inside the interval 204. Similarly, in some instances,readout signals can be transmitted, through the aperture 214, from areadout device associated with the qubit device 144A/144B located insidethe interval 204 to a signal receiver located outside theelectromagnetic waveguide system 104A. Apertures can also be provided atother locations. For example, apertures may additionally oralternatively be located adjacent to waveguide intersections 202 or atother locations in the electromagnetic waveguide system.

In the examples shown in FIGS. 6A and 6B, the waveguides defined by theelectromagnetic waveguide system 104A have rectangular cross-sections.As shown in FIG. 6B, the example rectangular cross-section of theinterval 204 has a width “a” along the y-axis and a height “b” along thez-axis. In the example shown, the largest transverse dimensiondetermines a frequency fc of the lowest frequency mode that canpropagate through the interval 204 of the waveguide. The frequency fc isreferred to as the cutoff frequency fc of the waveguide. In this manner,signals having frequencies above the cutoff frequency (f>fc) canpropagate through the waveguide, while signals having frequencies belowthe cutoff frequency (f<fc) evanesce in the waveguide. For this reason,signals having frequencies below the cutoff frequency (f<fc) that areinjected into the waveguide through the aperture 214 will be attenuated(e.g., exponentially) inside the waveguide from the aperture 214. Forexample, for a waveguide with rectangular cross-section havingdimensions a=0.5 cm and b=0.3 cm, the cutoff frequency is approximately30 GHz (fc 30 GHz). In some examples, the waveguides have otherdimensions and cutoff frequencies in other ranges.

In some implementations, a diagonal cross-section of the waveguideintersection 202 of two intersecting waveguides has a transversedimension a√2 which determines a minimum frequency (denoted fmin) thatis smaller than the cutoff frequency fc of the interval 204 (i.e.,fmin<fc). In the foregoing example, where dimensions of the waveguidewith rectangular cross-section are a=0.5 cm and b=0.3 cm, the minimumfrequency corresponding to the waveguide intersection 202's diagonalcross-section mode is approximately 24 GHz (fmin≈24 GHz).

FIG. 7 shows a portion of the interior volume of the exampleelectromagnetic waveguide system 104A. In the example shown, theelectromagnetic waveguide system includes a first subset of waveguidesi=1, 2, . . . oriented along the x-axis of a Cartesian coordinate systemthat intersect a second subset of waveguides j=1, 2, . . . orientedalong the y-axis of the Cartesian coordinate system. The waveguidesintersect at a 2D array of intersections 202-(i|j) shown in FIG. 7. Inthe example shown, signals having frequencies below the minimumfrequency (f≤fmin) that are injected into the electromagnetic waveguidesystem 104A through apertures located at a group of nearest-neighborintersections, e.g., 202-(i|j), 202-(i|j+1) and 202-(i+1|j), remainlocalized at the intersections where they are injected.

In some implementations, signals can be strongly localized to individualwaveguide intersections 202 if the signals' frequencies are between zeroand the minimum frequencies defined by the waveguide intersections 202,i.e., in the range of f=0 to f=fmin<fc, where fmin is a frequency of thelowest-lying resonant mode of the waveguide intersections 202, and fc isthe cutoff frequency of the intervals 204. In some implementations,disorder in the coupling strength between waveguide intersections 202 ofthe 2D lattice can be added by slightly altering the lateral dimensionsof the waveguide crossings or otherwise introducing small perturbationsof the frequencies of the modes. In some instances, localization ofspurious resonant modes at fmin can be further increased by dissipationin the waveguide intervals 204 connecting the intersections 202.

In the example shown in FIG. 7, the shading at the waveguideintersections 202-(i|j), 202-(i|j+1) and 202-(i+1|j) represents thespatial distribution of the electromagnetic field strength forelectromagnetic waves introduced into the interior volume of the examplewaveguide system 104A at the respective waveguide intersections202-(i|j), 202-(i|j+1) and 202-(i+1|j). In the example shown, theelectromagnetic waves are introduced at the frequency (fmin) thatcorresponds to the lowest-lying resonant mode of the waveguideintersections. The shading in FIG. 7 shows that the resultingelectromagnetic field strength drops to essentially zero within a shortdistance of the respective waveguide intersections 202-(i|j),202-(i|j+1) and 202-(i+1|j).

As shown in FIG. 7, because the electromagnetic waves have a frequency(fmin) that is less than the cutoff frequency (fc) of the waveguideintervals 204, the electromagnetic waves do not propagate in thewaveguide intervals 204. In particular, the waveguide intervals 204evanesce electromagnetic waves below the cutoff frequency (fc). In theexample shown, the field strength drops significantly in each directionfrom the respective waveguide intersections 202-(i|j), 202-(i|j+1) and202-(i+1|j). In some instances, when an electromagnetic wave isevanesced by a waveguide structure, the electromagnetic field strengthdrops exponentially along the main axis of the waveguide structure.

In the example shown in FIG. 7, the waveguide intervals 204 have a widthof 0.5 cm and a height of 0.3 cm; the waveguide intervals 204 define acutoff frequency (fc) of 29.98 GHz; and the waveguide intersections 202define a lowest-lying resonant mode frequency (fmin) of 24.42 GHz.Signals introduced at or below the cutoff frequency (fc) correspond toevanescent modes of the waveguide intervals 204, and therefore, thewaveguide intervals 204 suppress all such signals. In the example shown,signals having the frequency fmin are introduced at the waveguideintersections 202-(i|j), 202-(i|j+1) and 202-(i+1|j), and the signalstrength becomes negligible within a short distance of each respectivewaveguide intersection. In the particular example shown, theelectromagnetic field strength drops by approximately nine orders ofmagnitude (from 1.33(10)⁹ to below (10)⁰) before reaching the midpointof the adjacent waveguide interval 204.

In some implementations, the devices housed in the electromagneticwaveguide system 104 have operating frequencies well below the cutofffrequencies of the waveguide intervals, and the electromagnetic signalsthat control the devices correspond to evanescent modes of the waveguideintervals. Thus, the control signals are evanesced by the waveguideintervals, and they do not spatially propagate within the interiorvolume of the waveguide system. For instance, the electromagneticsignals introduced at a waveguide intersection can control a devicehoused at the waveguide intersection without introducing noise at otherintersections.

FIG. 8 shows a portion of an interior volume of an electromagneticwaveguide system 104B′ that includes a 3D lattice of intersectingwaveguides in which some of the intersections 202 have a size (along atleast one of two rectangular cross-section dimensions) that is differentfrom a size of other the intersections 202′. In the example shown, theinterior volume is viewed along one of the Cartesian axes, and the smallfeatures at the intersections 202 represent the waveguides extending inor out of the plane of the page. Here, a minimum frequency fmincorresponding to the diagonal cross-section of a first waveguideintersection 202 is different from a minimum frequency fmincorresponding to the diagonal cross-section of another waveguideintersection 202′ (i.e., fmin≠fmin). Further, in the example shown inFIG. 8, the 3D lattice of intersecting waveguides includes a subset ofintervals 204 that have continuous cross-sections (do not includediscontinuities) and another subset of intervals 204′ that havecross-section discontinuities 216. At cross-section discontinuities, asize (along at least one of two rectangular cross-section dimensions) ofthe cross-section of an interval 204′ changes discontinuously (e.g., ina stepwise fashion). Here, a cutoff frequency fc corresponding to thecross-section of the interval 204′ on one side of the discontinuity 216is different from a cutoff frequency f c corresponding to thecross-section of the interval 204′ on the opposing side of thediscontinuity 216 (i.e., fc≠fc).

In some instances, apertures 214 in an interval 204 of a waveguide or ata waveguide intersection 202 may produce sufficient dissipation toprovide strong localization of resonant modes. In some implementations,another source of dissipation is the finite loss tangent and resistivityof materials of various devices or components (e.g., a signal board)housed inside the 2D lattice of intersecting waveguides. Additionaldissipation in the intervals 204 of the 2D lattice of intersectingwaveguides may be added through incorporation of metallic (as opposed tosuperconducting) segments in the 2D or 3D lattice of intersectingwaveguides. Further, localization may be increased in some cases bydecoupling intersections 202, for instance, by decreasing the ratio ofthe waveguide cross section (e.g., the longer dimension of thecross-section) to the length of the interval 204; decreasing the ratiomay cause the intersections to be more decoupled.

In view of the above, the example electromagnetic waveguide system 104Athat includes a 2D lattice of intersecting waveguides can provide a highdegree (e.g., exponential) isolation of qubit devices 144A/144B of the2D device array 148A/148A′ arranged within the 2D lattice ofintersecting waveguides. In some cases, the isolation of the qubitdevices can be provided independent of the number of intersections 202of the 2D lattice of intersecting waveguides and independent of thenumber and the length of intervals 204 of the 2D lattice of intersectingwaveguides. Using the example 2D device array and the example 2D latticeof intersecting waveguides, the example systems 200A/200A′ can be used,in some instances, to fabricate large scale quantum processor cells 102for performing fault tolerant quantum computation with solid state qubitdevices 144A/144B and tunable coupler devices 142A/142B. Exampleimplementations of quantum processor cells 102 are described below.Moreover, the concepts can be extended directly to three-dimensions, forexample, to provide a high degree of (e.g., exponential) isolation ofqubit devices of a 3D device array arranged within a 3D lattice ofintersecting waveguides

FIG. 9 shows a plan view of a portion of an example quantum processorcell (QPC) 102B. The example QPC 102B represented in FIG. 9 includes anelectromagnetic waveguide system 104B that defines a 2D lattice ofintersecting waveguides. Here, a subset of the waveguides in the 2Dlattice (e.g., the ones oriented along the x-axis of a Cartesiancoordinate system) intersect another subset of the waveguides (e.g., theones oriented along the y-axis of the Cartesian coordinate system) atwaveguide intersections 202A. Moreover, the waveguides form intervals204A between the waveguide intersections 202A. In this manner, signalscommunicated into the interior volume of the waveguide system arestrongly localized to individual waveguide intersections 202A, forexample, if the signals' frequencies are between zero and thelowest-lying resonant mode of the intersection, i.e., in the range off=0to f=fmin<fc, where fmin is a frequency of the lowest-lying resonantmode of the intersections 202A and fc is the cutoff frequency of theintervals 204A.

The example QPC 102B shown in FIG. 9 includes a 2D device array 148Ahoused inside the electromagnetic waveguide system 104B. The example 2Ddevice array 148A includes qubit devices 144 located at nodes of the 2Ddevice array 148A and coupler devices 142 located along bonds (betweenthe nodes) of the 2D device array 148A. Further, the example QPC 102Bincludes a signal board 140A. The example signal board 140A communicatessignals to and from the devices of the 2D device array 148A. Forinstance, the signal board 140A can communicate control signals to thequbit devices and coupler devices, and communicate readout signals fromthe readout devices. The example signal board 140A also mechanicallysupports the devices of the 2D device array 148A inside the interiorvolume of the electromagnetic waveguide system 104B. Further, theexample QPC 102B also includes input connector hardware through whichcontrol signals can be delivered to the signal board 140A (e.g., from aninput signal processing system 128), and output connector hardware 138Bthrough which readout signals can be delivered from the signal board140A (e.g., to an output signal processing system 130).

In some implementations, signals that are configured to control thequbit devices 144A have frequencies fq, and signals that are configuredto control the tunable coupler devices 142A have frequencies ft. Invarious implementations, the coupler operating frequencies can be largerthan the qubit operating frequencies (fq<ft), or the qubit operatingfrequencies can be larger than the coupler operating frequencies(ft<fq). In the example 2D device array 148A shown in FIG. 9, readoutdevices associated with respective qubit devices 144A are arranged suchthat each of the readout devices is collocated with its qubit device ata respective node of the example 2D device array 148A where its qubitdevice is located. In some examples, signals that are configured tocontrol the readout devices associated with qubit devices 144A havefrequencies fr that are higher than both the qubit operating frequencies(fq) and the coupler operating frequencies (ft), such that fq<fr andft<fr. For these reasons, the devices in the 2D device array 148A areconfigured such that their operating frequencies and the frequencies(fq, fr and ft) of the control signals that operate them are smaller(e.g., ten times smaller) than fmin. For example, the devices can beconfigured such that fq<ft<fr<fmin<fc, such that ft<fq<fr<fmin<fc, or inanother manner. Thus, in some instances, individual qubit devices 144Ain the 2D device arrays 148A are shielded and isolated from all buttheir nearest-neighbors.

FIG. 10A shows a side cross-sectional view of the example signal board140A. The example signal board 140A is formed from a multilayersubstrate 218. The multilayer substrate 218 of the example signal board140A can include conducting layers separated by insulating layers. Theinsulating layers can include, for example, silicon, sapphire, fusedquartz, diamond, beryllium oxide (BeO), aluminum nitride (AlN), orothers insulative materials. In the example shown, ground planes 220 areformed by metal layers on outer (e.g., top and bottom) surfaces of themultilayer substrate 218 or inner surfaces (e.g., between two or more ofthe adjacent layers) of the multilayer substrate 218. The example signalboard 140A also includes thermalization posts 222 formed through thethickness of the signal board 140A. The example thermalization posts 222are thermally shorted to the outer and inner ground planes 220 tomaintain a bulk of the multilayer substrate 218 at a cryogenic operatingtemperature. Further, the example signal board 140A includesthermalization post contact areas 224 for application of pressureagainst additional bulk thermalization materials that may be in contactwith the signal board 140A. Furthermore, the example signal board 140Aincludes signal lines 225. The signal lines can be formed as patternedstripline or buried microstrip or other microwave transmission lines tocarry control or readout signals on interior layers of the multilayersubstrate 218. Additionally, the example signal board 140A includessignal board vias 226 that are configured to provide electrical contactand thermalization between various layers of the multilayer substrate218. A signal board may include additional or different features.

FIG. 10B shows a perspective view of the example signal board 140A. Asshown in FIG. 10B, the example signal board 140A includes contiguousareas 228, referred to as plateaus, and arms 230 that connectnearest-neighbor plateaus 228 and next-to-nearest-neighbor plateaus 228.Portions of the example signal board 140A between the plateaus 228 andthe arms 230 are vacant, such that the arms render the signal board 140Aa reticulated aspect. In this example, each plateau has fournearest-neighbor plateaus and four next-to-nearest-neighbor plateaus. Inthe example shown in FIG. 10B, next-to-nearest-neighbor plateaus areconnected through arms that extend diagonally to a qubit receptacle 232,and nearest-neighbor plateaus are directly connected through a pair ofarms that define a coupler receptacle 234. The qubit receptacles 232 areeach sized to support a qubit device 144 of the 2D device array 148A,and the coupler receptacles are each sized to support a coupler device142 of the 2D device array 148A. In some implementations, in whichreadout devices are collocated with respective qubit devices 144, thequbit receptacles 232 are each sized to support a qubit device 144 andits readout device. As shown in FIG. 10B, each of the qubit receptacles232 includes a perimeter frame that has a stepped inner profile, and issupported by four arms that extend diagonally from a surrounding groupof plateaus 228; and each of the coupler receptacles 234 includes a pairof sidewalls defined by a stepped profile of two parallel arms. A signalboard can include additional or different features, and the arms,receptacles, and other features of a signal board can be configured inanother manner.

FIG. 11A is an exploded view of a portion of the example QPC 102B shownin FIG. 9. The exploded view in FIG. 11A shows that the 2D lattice ofintersecting waveguides defined by the example electromagnetic waveguidesystem 104B is formed from a base portion 236 and a lid portion 238. Thebase portion 236 includes a base 208A and base wall structures 210Aextending vertically from the base 208A. The base wall structures 210Ainclude side surfaces that can be orthogonal to an upper surface of thebase 208A. The base wall structures 210A are arranged relative to oneanother such that their side surfaces form the lower half of the wallsthat define the waveguide intersections 202A and intervals 204A shown inFIG. 9. Further, the base wall structures 210A include upper ledgesurfaces that can be parallel to the upper surface of the base 208A. Thebase wall structures 210A are further arranged relative to one anothersuch that the plateau portions of the signal board 140A can rest on theupper ledge surfaces of the base wall structures 210A.

Similarly, the lid portion 238 includes a lid 212A and lid wallstructures 210B extending vertically from the lid 212A. The lid wallstructures 210B include side surfaces that are orthogonal to a lowersurface of the lid 212A. The lid wall structures 210B are arrangedrelative to one another such that their side surfaces form the upperhalf of the walls that define the waveguide intersections 202A andintervals 204A shown in FIG. 9. Further, the lid wall structures 210Binclude a lower ledge surface that is parallel to a lower surface of thelid 212A. The lid wall structures 210B are further arranged relative toone another such that the plateau portions of the signal board 140A canbe sandwiched between the upper ledge surfaces of the base wallstructures 210A and the lower ledge surfaces of the lid wall structures210B, as shown in FIG. 11B, which is a side cross-sectional view of theexample QPC 102B. FIG. 11B also shows that the example base 208A, thewall structures 210A, 210B and the lid 212A of the electromagneticwaveguide system 104B together enclose an interior volume 206 of the 2Dlattice of intersecting waveguides.

FIGS. 9 and 11A show that qubit devices 144 and coupler devices 142 ofthe 2D device array 148A can be supported by the signal board 140A toform rows of devices (e.g., along the x-axis of a Cartesian coordinatesystem) and columns of devices (e.g., along the y-axis of a Cartesiancoordinate system). In this manner, each qubit device 144 of the 2Ddevice array 148A has four adjacent coupler devices and fournearest-neighbor qubit devices. Moreover, each coupler device 142 of the2D device array 148A has two adjacent qubit devices. Here, separation ofthe qubit receptacles 232 and coupler receptacles 234 of the signalboard 140A are configured such that bonds of the 2D device array 148Ahave the same size and orientation as the intervals 204A of the 2Dlattice of intersecting waveguides; thus, the 2D device array 148A iscommensurate to the 2D lattice of intersecting waveguides. Moreover, thesignal board 140A is arranged relative to the electromagnetic waveguidesystem 104B to align the 2D device array 148A to the 2D lattice ofintersecting waveguides such that the nodes of the 2D device array 148Acoincide with the intersections 202A of the 2D lattice of intersectingwaveguides. In this manner, qubit devices 144 of the 2D device array148A are placed inside the electromagnetic waveguide system 104B atintersections 202A of the 2D lattice of intersecting waveguides, andcoupler devices 142 of the 2D device array 148A are placed inside theelectromagnetic waveguide system 104B along intervals 204A (betweenintersections 202A) of the 2D lattice of intersecting waveguides.

In the example shown in FIGS. 11A-11E, the signal board 140A includessignal board vias 226 (shown in FIG. 10A) that form a connection betweenthe base portion 236 and the lid portion 238 of the electromagneticwaveguide system. The holes 242 in the base portion 236 or the lidportion 238 (or both) can provide access to the signal board 140A forsending input signals into the signal board 140A and receiving outputsignals from the signal board 140A.

FIG. 11C is plan view of the portion of the example QPC 102B shown inFIG. 11A. FIG. 11C shows that at least a portion of the plateaus 228 ofthe signal board 140A in the example QPC 102B reside outside theinterior volume 206 of the electromagnetic waveguide system 104B. In theexample shown, the arms 230 that extend between next-to-nearest-neighborplateaus (and which support qubit receptacles 232) and the arms 230 thatextend between nearest-neighbor plateaus (and which define the couplerreceptacles 234) pass through the wall structures 210A (which partiallydefine the 2D lattice of intersecting waveguides) through the apertures240.

In some implementations, control lines extend through all or part of oneor more of the arms 230. The control lines can extend in the apertures240, and in some cases, through the full thickness of the wall. In thismanner, a control signal can be communicated into the interior volume206 of the electromagnetic waveguide system 104B from a plateau 228through an aperture 240 of the electromagnetic waveguide system 104B.For instance, a control signal can be communicated on a signal linehoused in an arm 230 that connects the plateau to a receptacle thatsupports a device (e.g., a qubit device 144 or a coupler device 142) towhich the control signal is addressed. Similarly, a readout signal canbe extracted from a qubit device 144 located inside the interior volume206 of the electromagnetic waveguide system 104B to a plateau 228through an aperture 240 of the electromagnetic waveguide system 104B.For instance, a readout signal can be communicated on a signal linehoused in an arm 230 that connects the qubit device 144 to the plateau228. In the example shown in FIGS. 11A-11E, the apertures are formed inthe side walls 210A, 210B. In this or other examples, apertures mayadditionally or alternatively be formed in the upper walls (through thelower surface of the lid 212A), in the lower walls (through the uppersurface of the base 208A), or both.

FIG. 11D is a perspective view of the example electromagnetic waveguidesystem 104B, and FIG. 11E is a zoom-in view of a portion of the same. Asshown in FIG. 11D, the example electromagnetic waveguide system 104B isformed by an assembly of two components. In particular, the exampleelectromagnetic waveguide system 104B is formed by mating, connecting,bonding or otherwise assembling the lid portion 238 with the baseportion 236. The assembly of the wall structures 210A, 210B, the base208A and the lid 212A define an interior volume 206 of a 2D lattice ofintersecting waveguides. Additionally, the wall structures 210A, 210Bdefine holes 242 through the lid portion 238 and through the baseportion 236. The holes 242 provide access to plateaus 228 of the signalboard 140A which are located outside the partially enclosed inner volume206 of the electromagnetic waveguide system 104B. The apertures 240 ofthe wall structures 210A, 210B described above in connection with FIG.11C are also shown in FIGS. 11D and 11E. When the electromagneticwaveguide system 104B is used in the QPC 102B, arms of the signal board140A that connect nearest-neighbor plateaus penetrate the apertures 240Ato deliver control signals from a plateau 228 to a coupling device 142;and arms of the signal board 140A that connect next-to-nearest-neighborplateaus penetrate the apertures 240B to deliver control signals from aplateau 228 to a qubit device 144 or to retrieve readout signals fromthe qubit device to the plateau 228.

Each of FIGS. 12A and 12B shows an example of an interval 204 of awaveguide of an example electromagnetic waveguide system. The exampleintervals 204 shown in FIGS. 12A and 12B include pass-throughstructures. FIG. 12A shows a first example pass-through structure 246,and FIG. 12B shows a second example pass-through structure 246A. In theexample shown, the side walls 210 are made from a conducting orsuperconducting material and partially define the boundary of theexample interior volume 206. The example pass-through structures 246,246A extend between two apertures 240A located on opposing side walls210. An outer surface of the pass-through structure 246, 246A can bemade from the same conducting or superconducting material as the sidewalls 210. In some cases, the outer surface of the pass throughstructures 246, 246A can be a thin film metal, a bulk metal, from a rowor array of via structures, or another structure. In the exampleillustrated in FIG. 12A, a multilayer board 243 includes a strip line244 and crosses the interior volume 206 of the waveguide through thepass-through structure 246. In this manner, a signal carried through thestrip line 244 is electromagnetically insulated from any qubit device144 or coupler device 142 that may be housed inside the interval 204adjacent to the pass-through structure 246. In the example illustratedin FIG. 12B, the pass-through structure 246A has an additional aperture248 on one of its side surfaces, such that the additional aperture opensto the interior volume 206 of the interval 204. Here, a multilayer board243A crosses the interior volume 206 of the waveguide through thepass-through structure 246, and a strip line 244A of the multilayerboard 243A ends at a location adjacent to the additional aperture 248 ofthe pass-through structure 246A. In this manner, a signal carriedthrough the strip line 244 can be delivered through the additionalaperture 248 to a qubit device 144 or coupler device 142 that may behoused inside the interval 204 adjacent to the pass-through structure246A. In some cases, other types of pass-through structures can be used.For instance, a pass-through structure can include multiple apertures,other types of boards, etc.

Example components and structures of the example QPC 102B have beendescribed above. Examples of methods for assembling the example QPC 102Bare described below.

FIGS. 13A-13G show aspects of an example process 250 for assembling theexample QPC 102B shown in FIG. 9. Some of the operations 250-1 through250-6 of the example process 250 can be performed in a different orderthan as illustrated here, can be performed concurrently or can bereplaced by other operations. Further, the example process 250 mayinclude additional operations performed prior to, after or interspersedbetween the operations illustrated here. In some instances, one or moreof the operations 250-1 through 250-6 of the example process 250 can beused in the assembly of other quantum processor cells.

At 250-1, a base portion 236 of an electromagnetic waveguide system 104Bis provided. FIG. 13A is a partial perspective view of the base portion236 of the example electromagnetic waveguide system 104B. In thisexample, the base portion 236 includes a base 208A and base wallstructures 210A. In some implementations, the base 208A and base wallstructures 210A are formed from a metallic conductor material, asuperconductor material, or a combination of these and other materials.In some implementations, the base 208A and base wall structures 210A canbe formed by deposition of thin film metallic or superconductingmaterials on a micro-machined silicon substrate, a pattered dielectricor insulating substrate, or other material system. In some cases, someportions of surfaces of the foregoing base 208A and base wall structures210A are coated with a layer of superconductor material. In otherimplementations, the base 208A and base wall structures 210A are formedfrom a superconductor material.

The example base wall structures 210A are distributed on the base 208Ato form intersections and intervals of a 2D lattice of intersectingwaveguides. Moreover, the example base wall structures 210A encloseholes 242A (or openings) of the base 208A. The base wall structures 210Ahave an upper ledge surface that is parallel to an upper surface of thebase 208A. The upper ledge surface of each base wall structure 210Adefines first channels oriented in directions toward nearest-neighborbase wall structures. The first channels represent a lower half of afirst type of apertures 240A described above in connection with FIGS.11D and 11E. Additionally, the upper ledge surface of each base wallstructure 210A defines second channels oriented in directions towardnext-to-nearest-neighbor base wall structures. The second channelsrepresent a lower half of a second type of apertures 240B describedabove in connection with FIGS. 11D and 11E.

At 250-2, a first sub-assembly (236+140A) is formed from the baseportion 236 and a signal board 140A. FIG. 13B is a perspective view of aportion of the first sub-assembly (236+140A). The example signal board140A was described above in connection with FIGS. 10A-10B. Here, theplateaus 228 of the signal board 140A are mated with the ledge surfacesof the base wall structures 210A over the holes 242A of the base 208Aenclosed by the base wall structures. Arms 230 of the signal board 140Athat define a coupler receptacle 234 located between nearest-neighborplateaus rest in the lower half of the apertures 240A. Other arms 230that extend to a qubit receptacle 232 located betweennext-to-nearest-neighbor plateaus rest in the lower half of theapertures 240B. In this manner, the first sub-assembly (236+140A) hascoupler receptacles located in intervals (between intersections) of the2D lattice of intersecting waveguides and qubit receptacles located atintersections of the 2D lattice of intersecting waveguides. In theexample shown, the top half of the waveguide system (the lid 212A) canmake good electromagnetic contact with the lower half of the waveguidesystem (the base 208A). In this example, the contact points where thebase 208A can make electromagnetic contact with the lid 212A areprovided on the ledges of the wall structures 210A, in particular, atraised portions on either side of the apertures 240A and 240B.Electrical contact between the base 208A and lid 212A may be provided inanother manner.

At 250-3, a second sub-assembly (236+140A+148A) is formed from the firstsub-assembly (236+140A) and a 2D device array 148A. FIG. 13C is aperspective view of the second sub-assembly (236+140A+148A). Here, qubitdevices 144 of the example 2D device array 148A are placed in the qubitreceptacles 232 located at intersections of the 2D lattice ofintersecting waveguides. In some implementations, in which readoutdevices are collocated with respective qubit devices 144, a qubit deviceand its readout device are placed in each of the qubit receptacles 232.For example, the collocated qubit device 144 and readout device can beformed on the same chip. As another example, the collocated qubit device144 and readout device can be formed on separate chips. Separate chipscan be located vertically above and below one another at the qubitsites/lattice intersections. Also, coupler devices 142 of the example 2Ddevice array 148A are placed in the coupler receptacles 234 located inthe intervals (between the intersection) of the 2D lattice ofintersecting waveguides.

At 250-4, the qubit devices 144 and the coupler devices 142 of theexample 2D device array 148A are connected with signal lines of thesignal board 140A. FIG. 13D is another perspective view of the secondsub-assembly (236+140A+148A), where some top layers of the examplesignal board 140A have been hidden from view. Here, signal linesoriginate at a connection junction 251 associated with each plateau 228and extend to respective qubit devices 144 or the coupler devices 142 inthe following manner. For example, a coupler signal line 225B isembedded between layers of the signal board 140A and extends from theconnection junction 251 of a plateau 228 to a coupler device 142 alongan arm 230 that enters the interior volume of an interval of the 2Dlattice of intersecting waveguides through an aperture 240A. The couplersignal line 225B carries a coupler control signal from the plateau 228located outside the electromagnetic waveguide system 104B to a couplercontrol input port (as shown in FIG. 3A) of the coupler device 142located inside the electromagnetic waveguide system. Coupler signallines 225B can be DC-coupled (e.g., by mutual inductive coupling ordirect current coupling) to corresponding coupler devices 142. Asanother example, a qubit signal line 225A is embedded between layers ofthe signal board 140A and extends from the connection junction 251 ofthe plateau 228 to a qubit device 144 along another arm 230 that entersthe interior volume of an interval of the 2D lattice of intersectingwaveguides through apertures 240B. The qubit signal line 225A carries aqubit control signal from the plateau 228 located outside theelectromagnetic waveguide system 104B to a qubit+readout control port(as shown in FIG. 3A) of the qubit device 144 located inside theelectromagnetic waveguide system. Qubit signal lines 225A can beAC-coupled to corresponding qubit devices 144. In some implementationsof the process 250, the operation 250-4 can be performed betweenoperations 250-2 and 250-3.

At 250-5, connection junctions 251 located at plateaus 228 of a signalboard 140A are connected to respective multiple signal connectors 138A(also referred to as vertical interconnects). FIG. 13E is a perspectiveview of a portion of the second sub-assembly (236+140A+148A) that showsmultiple signal connectors 138A connected adjacent respective plateaus228 of the example signal board 140A. Each of the multiple signalconnectors 138A is arranged and configured to create multiple electricalconnections between qubit signal lines 225A and coupler signal lines225B that are routed horizontally through the signal board 140A andcorresponding vertical transmission lines or interposer structures thateither deliver qubit control signals, qubit readout signals and couplercontrol signals from input processing hardware 132 located outside theQPC 102B or return readout signals from qubit devices to outputprocessing hardware 134 located outside the QPC 102B. Examples ofmultiple signal connectors 138A are described below in connection withFIGS. 18A-18C. In some implementations, the vertical transmissionlines—which can be coaxial or ribbon type transmission lines, forinstance—connect the multiple signal connectors 138A with input oroutput processing hardware 132, 134 located outside the example QPC102B. In some implementations of the example process 250, the operation250-5 can be performed between operations 250-2 and 250-3 or betweenoperations 250-3 and 250-4.

At 250-6, an electromagnetic waveguide system 104B of the QPC 102B isformed. FIG. 13F is a lateral cross-section of the QPC 102B. Here, a lidportion 238 of the electromagnetic waveguide system 104B is mated withthe base portion 236 thereof to form an interior volume 206 of the 2Dlattice of intersecting waveguides. Portions of the example signal board140A that support the 2D device array 148A are enclosed within theinterior volume 206 while the plateaus 228 of the signal board aresandwiched between the base portion 236 and the lid portion 238. FIG.13G is a perspective view of a portion the example QPC 102B. Here, lidwall structures 210B of the lid portion 238 enclose holes 242B (oropenings) of the lid 212B. The holes 242B allow access to respectivemultiple signal connectors 138A. In some implementations, thermalizationblocks can be introduced in the holes 242B to extract heat generatedduring operation of the QPC 102B. In some implementations, the signalboard 140A may extend outside the waveguide system, where additionalinterconnect plateaus may be formed.

Examples of QPCs fabricated by enclosing 2D device arrays 148A inelectromagnetic waveguide systems 104A that includes a 2D lattice ofintersecting waveguides have been described above. In some cases, suchQPCs can be operated to solve a multitude of problems, for instance, byperforming fault tolerant quantum computation based on algorithms thatare optimized or otherwise adapted to operate on two-dimensional qubitarrays. Some algorithms are optimized or otherwise adapted to operate onthree-dimensional qubit arrays, and in some cases, QPCs that enclosethree-dimensional qubit arrays can be used for quantum computation. Forinstance, three-dimensional qubit arrays may be useful for performingfault tolerant quantum computation, in some instances, with highereffectiveness than other types of quantum computing systems.

In some implementations, all or part of the portion of the device array148 shown in FIG. 3A can be copied multiple times, as a unit cell, toextend the device array 148 in space (e.g., in layers parallel to thex-y plane that are distributed along a z-axis of a Cartesian coordinatesystem or as layers parallel to the x-y plane that intersect layersparallel to the y-z plane). In some cases, such a three-dimensional (3D)device array may allow each qubit device to be independently controlledand measured without introducing crosstalk or errors on other qubitdevices in the 3D device array. In some cases, nearest-neighbor pairs ofqubit devices in the 3D device array can be addressable with two-qubitgate operations capable of generating entanglement, independent of allother such pairs in the 3D device array. In some instances, the devicearray may also be extended within the x-y plane to form systems ofarbitrarily large number of qubits and couplers within a single modularelectromagnetic waveguide system.

To shield the devices of a 3D device array from each other and from anelectromagnetic environment, the 3D device array can be arranged insidean electromagnetic waveguide system 104C that includes a 3D lattice ofintersecting waveguides. FIG. 14A shows a portion of the interior volumeof an example electromagnetic waveguide system 104C. In particular, FIG.14A is a perspective view of a portion of an example electromagneticwaveguide system 104C that includes a first set of waveguides i=1, 2, .. . oriented along the x-axis of a Cartesian coordinate system, a secondset of waveguides j=1, 2, . . . oriented along the y-axis of theCartesian coordinate system, and a third set of waveguides k=1, 2, . . .oriented along the z-axis of the Cartesian coordinate system, where thewaveguides intersect each other at a 3D array of waveguide intersections202-(i|j|k). As shown in FIG. 14A, the waveguide intersections202-(i|j|k) are separated by waveguide intervals 204.

In some implementations, by forming such 3D device arrays, large-scalesystems of arbitrarily large numbers of qubits and couplers can beproduced within a single modular electromagnetic waveguide system forperforming large scale fault-tolerant quantum computing and quantuminformation storage.

The example 3D device array 148B may include devices housed at thewaveguide intersections 202, in the intervals 204 between the waveguideintersections 202, or a combination of these and other locations. Forinstance, either a qubit device or a coupler device can be placed at thewaveguide intersections 202 shown in FIG. 14A. Here, the 3D lattice ofintersecting waveguides is geometrically commensurate with the 3D devicearray 148B. In the example shown, the 3D device array 148B is alignedwith the 3D lattice of intersecting waveguides such that the nodes ofthe 3D device array 148B coincide with the waveguide intersections ofthe 3D waveguide lattice. In some implementations, qubit devices of the3D device array are placed inside the electromagnetic waveguide system104C at the waveguide intersections 202-(i|j|k) of the 3D lattice ofintersecting waveguides, and the coupler devices of the 3D device arrayare placed inside the electromagnetic waveguide system 104C alongintervals 204, between intersections 202-(i|j|k), of the 3D lattice ofintersecting waveguides. In other implementations, the coupler devicesof the 3D device array are placed inside the electromagnetic waveguidesystem 104C at intersections 202-(i|j|k) of the 3D lattice ofintersecting waveguides and the qubit devices of the 3D device array areplaced inside the electromagnetic waveguide system 104C along intervals204, between intersections 202-(i|j|k), of the 3D lattice ofintersecting waveguides.

FIG. 14B shows a portion of the interior volume 206 of theelectromagnetic waveguide system 104C near an example waveguideintersection 202-(i|j|k). In the portion shown in FIG. 14B, the interiorvolume 206 of the electromagnetic waveguide system 104C is enclosed bythree waveguides that intersect at the waveguide intersection202-(i|j|k), such that a first of the three waveguides has two intervals204-x along the x-axis, a second of the three waveguides has twointervals 204-y along the y-axis, and a third of the three waveguideshas two intervals 204-z along the z-axis.

In the example shown in FIG. 14B, the intervals 204 of the 3D lattice ofintersecting waveguides have rectangular cross-sections. In the exampleshown, the largest dimension of the two-dimensional rectangularcross-section (in this example the width) determines a cutoff frequencyfc. In this manner, signals having frequencies above the cutofffrequency (f>fc) can propagate through the waveguide, while signalshaving frequencies below the cutoff frequency (f<fc) evanesce in thewaveguide. For this reason, signals having frequencies below the cutofffrequency (f<fc) that are injected into the waveguide (e.g., through anaperture located at or near a waveguide intersection 202-(i|j|k)) willbe attenuated (e.g., exponentially) inside the waveguide from theaperture.

In the example shown in FIG. 14, the shading around the waveguideintersection 202-(i|j|k) represents the spatial distribution of theelectromagnetic field strength for electromagnetic waves introduced intothe interior volume of the example waveguide system 104B at theintersection 202-(i|j|k). In the example shown, the electromagneticwaves are introduced below the cutoff frequency (fc). The shading inFIG. 14 shows that the electromagnetic waves are evanesced, and theelectromagnetic field strength drops to essentially zero within a shortdistance of the waveguide intersection 202-(i|j|k).

In the example shown in FIG. 14, for an interval 204 of the waveguidewith rectangular cross-section having a width of 0.5 cm and a height of0.3 cm, the cutoff frequency is approximately 30 GHz (fc≈30 GHz).Additionally, in the example shown, a largest diagonal cross-section ofthe waveguide intersection 202-(i|j|k) of three intersecting waveguideshas a transverse dimension that defines a minimum frequency fmin, whichis less than the cutoff frequency fc of the interval 204 (i.e.,fmin<fc). In the example shown in FIG. 14B, where the rectangularcross-section has a width of 0.5 cm and a height of 0.3 cm, the minimumfrequency fmin corresponding to the diagonal cross-section of thewaveguide intersection 202-(i|j|k) is fmin≈25.7 GHz.

In some instances, signals having frequencies below the minimumfrequency (f<fmin) that are injected into the electromagnetic waveguidesystem 104A through apertures located at waveguide intersections, e.g.,202-(i|j|k), 202-(i|j−1|k) and 202-(i−1|j|k), remain localized at theintersections where they are injected. In this manner, the 3D lattice ofintersecting waveguides can provide high (e.g., exponential)electromagnetic isolation between an array site (i|j|k) and its sixnearest-neighbor array sites (i−1|j|k), (i|j−1|k), (i|j|k−1), etc.Moreover, individual qubit devices in the 3D device array can beshielded and isolated, such that they only interact with other qubitdevices when selectively coupled to nearest-neighbors by the couplerdevices; and all qubit devices can be isolated from the externalelectromagnetic environment. In some cases, the isolation of the qubitdevices can be provided independent of the number of intersections202-(i|j|k) of the 3D lattice of intersecting waveguides and independentof the number and the length of intervals 204 of the 3D lattice ofintersecting waveguides. Additionally, apertures formed in the walls ofthe lattice of intersecting waveguides can provide ports to inject orextract (or both) electromagnetic signals for control or measurement (orboth).

FIG. 15 is a perspective view of an example electromagnetic waveguidesystem 104C that defines a 3D lattice of intersecting waveguides, whichcan be used in a QPC 102C. In this example, the three-dimensional devicearray and other components in the QPC 102C can be formed by or adaptedfrom an interpenetrated arrangement of multiple two-dimensional QPCs102B. In the example illustrated in FIG. 15, the QPC 102C includes afirst set of two-dimensional systems 202B-(x-y) that are orientedparallel to a plane (x-y) of a Cartesian coordinate system, and a secondset of two-dimensional systems 202B-(y-z) that are oriented parallel toa plane (y-z) of the Cartesian coordinate system. Here, thetwo-dimensional systems 202B-(y-z) intersect the two-dimensional systems202B-(x-y) along rows in the (x-y) plane, and the two-dimensionalsystems 202B-(x-y) intersect the two-dimensional systems 202B-(y-z)along layers in the (y-z) plane. In this manner, the example arrangementillustrated in FIG. 15 forms the 3D array of intersections 202-(i|j|k)shown in FIG. 14A. The electromagnetic waveguide system 104C formed inthis manner can house a 3D device array that includes qubit devices 144and coupler devices 142 as part of an example QPC 102C. For example, insome instances, the example QPC 102C can be used to perform faulttolerant quantum computation or quantum information storage based onalgorithms and protocols optimized to work on three-dimensional qubitarrays.

Examples of QPCs 102B and 102C fabricated by enclosing multidimensionaldevice arrays in an electromagnetic waveguide system 104 that includes acommensurate lattice of intersecting waveguides have been describedabove. Techniques for delivering control signals to a QPC, for example,by an input signal processing system 128, and for retrieving readoutsignals from a QPC, for example, by an output signal processing system130, are described below.

FIGS. 16A-16F show aspects of an example system 252 that includes a QPCassembly with an electromagnetic waveguide system. The components of theexample system 252 shown in the figures also includes a portion of anexample output signal processing subsystem. FIG. 16A is a topcross-sectional view of the example QPC assembly at Z=0. FIG. 16B is aside cross-sectional view of the example QPC assembly at Y=0 and Y=±4.FIG. 16C is a top cross-sectional view of the example QPC assembly atZ=+1. FIG. 16D is a top cross-sectional view of the example QPC assemblyat Z=−1; FIG. 16E is a side cross-sectional view of the example QPCassembly at Y=±1 and Y=±3. FIG. 16E is a side cross-sectional view ofthe example QPC assembly at Y=±2. In some instances, the examplesstructures shown in FIGS. 16A-16F can be adapted to createthree-dimensional electromagnetic waveguide systems andthree-dimensional device arrays.

The example waveguide system shown in FIGS. 16A-16F includes a 2Dlattice of intersecting waveguides, with a portion of an output signalprocessing subsystem. The system 252 includes a 2D device array of qubitdevices 144C and coupler devices 142C arranged inside the 2D lattice ofintersecting waveguides. In this example, the 2D device array is locatedin the (x-y) plane of a Cartesian coordinate system. As shown in FIG.16A, each of the qubit devices 144C of the 2D device array has adedicated readout device 146C. As shown in FIGS. 16A and 16E, thereadout devices 146C are arranged in a 2D readout array located in aplane that is parallel to and spaced apart along the z-axis from theplane of the 2D device array.

As shown in FIGS. 16E and 16F, the output signal processing subsystemthat is part of the example system 252 can include amplifier circuits256 configured to amplify qubit readout signals produced by the readoutdevices 146C. In some implementations, the amplifier circuits 256 areimplemented as parametric amplifiers. A parametric amplifier can beconfigured to amplify an input signal when the amplifier is suppliedwith an electromagnetic pump signal. When the amplifier circuits 256 maybe implemented as parametric amplifiers, the output signal processingsubsystem may also include pump circuits 258 coupled to respectiveamplifier circuits. In the example system 252, the amplifier circuits256 can be implemented as parametric amplifier devices. Further, thepump circuits 258 used to drive the parametric amplifier devices 256 canbe implemented as pump devices.

In the example system 252, the qubit devices 144C and coupler devices142C of the 2D device array are mechanically supported by a receptacleboard 254. The receptacle board 254 can be a silicon wafer, a sapphirewafer or can be formed from other non-conductive materials. Thereceptacle board 254 includes qubit receptacles 232A and couplerreceptacles 234A. Each of the qubit receptacles 232A can be formed as aslot in the receptacle board 254 that is sized to receive a qubit device144C. In this example, the qubit receptacles 232A are arranged on thereceptacle board 254 at nodes of a 2D array, such that when held in thequbit receptacles, the qubit devices 144C form the nodes of the 2Ddevice array. Moreover, each of the coupler receptacles 234A can beformed as a slot in the receptacle board 254 that is sized to receive acoupler device 142C. In this example, the coupler receptacles 234A arearranged on the receptacle board 254 between the nodes of a 2D array,such that when held in the coupler receptacles, the coupler devices 142Cform the bonds of the 2D device array. Areas of the receptacle board 254located between the coupler receptacles 234A are referred to as plateaus228A of the receptacle board. The plateaus 228A may include conductiveor superconductive vias, e.g., oriented orthogonal to the (x-y) plane,to create conductive paths between opposing outer surfaces of thereceptacle board 254 at the locations of the plateaus 228A.

As shown in FIG. 16B, the base 208B supports the receptacle board 254,which in turn supports the 2D device array. The receptacle board 254 issandwiched between the base 208B and a flange 255. The flange 255includes flange wall structures 210C. The flange wall structures 210Chave mating surfaces that can mate and form an electrical, mechanical orthermal contact with the plateaus 228A of the receptacle board 254 andside surfaces orthogonal to the mating surfaces. FIG. 16C is across-section parallel to the (x-y) plane of the flange 255. Thecombination of FIGS. 16B-16C shows that the side surfaces of the flangewall structures 210C form walls that enclose an interior volume 206 ofthe electromagnetic waveguide system. Moreover, the combination of FIGS.16A-16C shows that the 2D lattice of intersecting waveguides defined bythe side surfaces of the flange wall structures 210C is commensuratewith the 2D device array supported by the receptacle board 254. In theexample system 252, the qubit devices 144C are arranged at intersectionsof the 2D lattice of intersecting waveguides and the coupler devices142C are arranged on intervals (between the intersections) of the 2Dlattice of intersecting waveguides.

The cross-section of the example system 252 in the (x-z) plane, as shownin FIG. 16B, represents a slice of the example system 252 that crossesthrough intervals of the 2D lattice of intersecting waveguides andcoupler devices 142C housed therein. In the example shown, couplersignal lines configured to deliver coupler control signals to couplerdevices 142C are DC-coupled (e.g., by mutual inductive coupling or bydirect current coupling) to coupler control input ports 154A. FIG. 16Dis a cross-section parallel to the (x-y) plane of the base 208B. FIG.16D shows that the base 208B has coupler apertures arranged to allow forthe coupler signal lines to reach the coupler control input ports 154Afrom an input signal processing system.

The cross-sectional view shown in FIG. 16E crosses through a waveguideoriented in the y-direction and shows a row of waveguide intersectionsand intervals. In this manner, this slice also crosses through the qubitdevices 144C hosted at the waveguide intersections and the couplerdevices 142C hosted inside the waveguide intervals. Along the view ofthe example system 252 shown in FIG. 16E, the interior volume 206 isenclosed between the flange 255 and the base 208B. In the example shown,qubit signal lines configured to deliver qubit control signals to qubitdevices 144C are AC-coupled through a coupling capacitance to qubitcontrol ports 156A. As shown in FIG. 16D, the base 208B has qubitapertures arranged to allow for the qubit signal lines to reach thequbit control ports 156A from the input signal processing system.

FIGS. 16B and 16E show that the example system 252 also includes a lidportion 212B positioned such that the flange 255 is sandwiched betweenthe receptacle board 254 and the lid portion 212B. The lid portion 212Bincludes readout receptacles to hold readout devices 146C adjacent to aninterface between the lid portion and the flange. Readout control signallines configured to deliver readout control signals to readout devices146C can be AC-coupled to readout control ports 156B. The lid portion212B has readout control apertures arranged to allow for the readoutcontrol signal lines to reach the readout control ports 156B from theinput signal processing system.

In the example shown, the readout receptacles form a 2D array thataligns with the 2D array of qubit receptacles 232A on the receptacleboard 254. Moreover, the flange 255 has a 2D array of readout aperturesaligned to both the 2D array of readout receptacles on the lid portion212B and the 2D array of qubit receptacles on the receptacle board 254.In this manner, each of the readout devices 146C can be capacitivelycoupled, through a respective readout aperture, with a respective qubitdevice 144C to enable the state of the respective qubit device to beprobed. A qubit readout signal that carries information about a qubitdevice 144C can be output by its associated readout device 146C at areadout output port. The readout output port is coupled with one of theamplifier circuits 256 of the example system 252. As shown in FIG. 16A,the example amplifier circuit 256 is laterally displaced in the x-yplane from a location of the readout device 146C, and the amplifiercircuit 256 is represented with a dashed line in FIG. 16E.

The example cross-section shown in FIG. 16F crosses through intervals ofthe 2D lattice of intersecting waveguides and coupler devices 142Choused therein. The example cross-section shown in FIG. 16F also crossesthrough parametric amplifier devices 256 and pump devices 258 stackedabove plateaus 228A of the receptacle board 254.

As shown in FIG. 16F, the example flange 255 includes amplifierreceptacles to hold the parametric amplifier devices 256. In thismanner, when the lid portion 212B is mated with the flange 255, theparametric amplifier devices 256 are held adjacent to an interfacebetween the flange 255 and the lid portion 212B. The amplifierreceptacles form a 2D array with nodes located above the plateaus 228Aof the receptacle board 254. In this manner, each of the parametricamplifier devices 256, when held in an amplifier receptacle, is operablycoupled to four nearest-neighbor readout devices 146C. Further, the lidportion 212B includes pump receptacles to hold the pump devices 258 in aplane of the lid portion 212B parallel to the (x-y) plane between the 2Darray of readout receptacles and the lid portion's outer surface.Moreover, the pump receptacles form a 2D array on the lid portion 212Bthat aligns with a 2D array of amplifier receptacles on the flange 255.

Readout signals received by each of the parametric amplifier devices 256from respective readout output ports of its four nearest-neighborreadout devices 146C can be amplified concurrently or sequentially byintegrating a multiplexing function as part of each of the parametricamplifier devices 256. In some implementations, the parametric amplifierdevice 256 can use frequency multiplexing to concurrently amplify thereceived readout signals, because frequencies of readout signals fromthe four nearest-neighbors of a parametric amplifier device 256 aredifferent from each other (e.g., as described below in connection withFIGS. 23A, 26 and others). In other implementations, the parametricamplifier device 256 can use time multiplexing to sequentially amplifythe received readout signals. In some implementations, an amplifier withoperational bandwidth including the frequency of all associated readoutsignals can be used.

In some implementations, components of a QPC (e.g., a lid portion, abase portion, a flange, etc.) are configured to accommodate devices thatcan process (e.g., amplify) readout signals immediately outside theinterior volume of the electromagnetic waveguide system. Suchconfigurations may, in some cases, result in significant reduction ofthe overall noise temperature of the amplification process due toelimination of noise that would be caused by transporting “raw”(unprocessed) readout signals for processing by an output signalprocessing subsystem located remotely from the QPC. Other exampletechniques described below combine the beneficial aspect of processingreadout signals in close proximity to a QPC having another structure(e.g., the structures shown in FIGS. 9, 11A, 13F, or other QPCstructures).

FIGS. 17A-17B show aspects of an example quantum computing system thatincludes a signal delivery subsystem and an electromagnetic waveguidesystem. FIG. 17A is a schematic diagram showing an example signal flowin the system 260, and FIG. 17B is a perspective view showing aspects ofcomponents represented schematically in FIG. 17A. As shown in FIGS. 17Aand 17B, the signal flow can be performed by a signal delivery system106B in connection with the example QPC 102B, which includes anelectromagnetic waveguide system 104B that defines a 2D lattice ofintersecting waveguides. The signal flow shown in FIG. 17A may beadapted for use with other types of systems.

The example system 260 operates in a cryogenic temperature regime, forexample, at low operational temperatures T_op (e.g., T_op being lessthan 60K, 3K, 800 mK, 150 mK, 10 mK) and under conditions that aresubject to very low electromagnetic and thermal noise. Such operationalconditions can be achieved in a QPC environment 101, as described abovein connection with FIG. 2. In some instances, the example system 260 canreceive control signals (e.g., write and read signals) through inputcontrol system connector hardware 126A from a signal generator system120 that is operated under an ambient environment (e.g., at higheroperational temperatures, e.g., T_op>240K). In some instances, theexample system 260 can transmit pre-processed or processed readoutsignals through output control system connector hardware 126B to asignal processor system 124.

In the example shown, the signal delivery system 106B includes an inputsignal processing system 128A and an output signal processing system130A. The input signal processing system 128A is configured to receiveand either pre-process or process control signals delivered by thesignal generator system 120 through the input control system connectorhardware 126A. The control signals can be delivered by the input signalprocessing system 128A to the QPC 102B through QPC input connectorhardware 136B. In some implementations, some of the incoming signals maybe routed horizontally within the signal board 140A (e.g., in both theleft and right directions, or other directions within the plane of thesignal board 140A).

In some instances, incoming signals (e.g., readout control signals)cause the quantum processor cell 102B to produce output signals that arerouted to the output signal processing system 130A; some incomingsignals (e.g., coupler control signals, qubit control signals) do notcause the quantum processor cell 102B to produce output signals that arerouted to the output signal processing system 130A. In some instances,readout signals from readout devices inside the QPC 102B are deliveredby the QPC 102B to the output signal processing system 130A through QPCoutput connector hardware 138B. The output signal processing system 130Ais configured to either pre-process or process the readout signals andto deliver the readout signals to the signal processor system 124.

In the example system 260, the example QPC 102B includes a 2D devicearray 148A supported inside an interior volume 206 of theelectromagnetic waveguide system 104B by a signal board 140A, as shown,for example, in FIGS. 9, 11A, and 13C-13E. The example electromagneticwaveguide system 104B includes holes (e.g., 242A) in a base portion(e.g., 236) adjacent to input plateaus (e.g., some of plateaus 228) ofthe signal board 140A, and at least a portion of the plateaus arelocated outside the interior volume 206 of the electromagnetic waveguidesystem 104B. The holes of the base portion can house, outside theinterior volume 206 of the electromagnetic waveguide system 104B, QPCinput connector hardware 136B. In the example illustrated in FIG. 17B,the QPC input connector hardware 136B includes an array of inputvertical interconnects 136B, where each of the input verticalinterconnects has an input end and an opposing, output end, and isformed from multiple wires directed from the input end to the outputend. In the example system 260, a respective input vertical interconnect136B is disposed in each hole of the base portion of the electromagneticwaveguide system 104B, such that the input end of the input verticalinterconnect 136B is coupled with the input signal processing system128A and the output end of the input vertical interconnect 136B iscoupled with an input connection junction (e.g., some of connectionjunction 251) at a respective input plateau of the signal board 140A.

Similarly, the example electromagnetic waveguide system 104B includesholes (e.g., 242B) in a lid portion (e.g., 238) distributed adjacent tooutput plateaus (e.g., other plateaus 228) of the signal board 140A, andat least a portion of the plateaus are located outside of the interiorvolume 206 of the electromagnetic waveguide system 104B. The holes ofthe lid portion can house, outside the interior volume 206 of theelectromagnetic waveguide system 104B, QPC output connector hardware138B. In the example illustrated in FIG. 17B, the QPC output connectorhardware 138B includes another array of output vertical interconnects138B, where each of the output vertical interconnects has an input endand an opposing, output end, and is formed from multiple wires orconductive paths directed from the input end to the output end. In theexample system 260, a respective output vertical interconnect 138B isinserted in each hole of the lid portion of the electromagneticwaveguide system 104B, such that the input end of the output verticalinterconnect 138B is coupled with an output connection junction (e.g.,other connection junctions 251) at a respective output plateau of thesignal board 140A and the output end of the output vertical interconnect138B is coupled with the output signal processing system 130A. A numberof wires of an input vertical interconnect 136B can be the same as ordifferent from a number of wires of an output vertical interconnect138B. Also, a type of the wires (material, thickness, etc.) of the inputvertical interconnect 136B can be the same as or different from a typeof the wires of the output vertical interconnect 138B. Wires orconductive paths may be formed, for example, by vias, by interconnectpins, an interposer board, or other structures.

FIGS. 18A-18C show examples of input and output connector hardware forthe example QPC 102B. FIG. 18A is a perspective view of the example baseportion 236A that includes vertical interconnects 136B, and FIG. 18B isa perspective view showing the lid portion 238A that includes verticalinterconnects 138B. FIG. 18C shows a perspective view of internalcomponents of the example electromagnetic waveguide system shown in FIG.18B.

In the example shown in FIG. 18A, the input vertical interconnects 136Breside in the holes (e.g., 242A) formed by base wall structures 210A ofthe base portion 236A of the electromagnetic waveguide system 104B. Insome instances, the input vertical interconnects 136B may be installedin the base portion 236A, for example, between operations 250-1 and250-2 of the example process 250 shown in FIGS. 13A-13G. The inputvertical interconnects 136B may be installed in another manner or atother points in an assembly process. The input vertical interconnects136B can mate with (e.g., contact) input plateaus 228B of the examplesignal board 140A. In some cases, holes of the remaining base wallstructures 210A′ of the base portion 236A that will be mated with outputplateaus 228C of the example signal board 140A may be plugged or coveredwith base plugs 266.

As shown in the example shown in FIG. 18B, the output verticalinterconnects 138B are installed in the lid portion 238A. For instance,output vertical interconnects 138B may be installed in a manner that isanalogous to the installation of the input vertical interconnectsdescribed above. In some cases, the output vertical interconnects 138Bmay be installed in the lid portion 238A, for example, between or duringa combination of operations 250-5 and 250-6 of the example process 250shown in FIGS. 13A-13G. The output vertical interconnects 138B may beinstalled in another manner or at other points in an assembly process.

In the perspective view shown in FIG. 18C, portions of the QPC 102B fromFIG. 18B are hidden from view; in particular, portions located above aslice that crosses the lid portion 238A and the input verticalinterconnects 136B are hidden from view. As demonstrated by FIGS. 18Band 18C, the example 2D device array 148A is supported by the examplesignal board 140A, and the signal board 140A is sandwiched between thebase portion 236A and the lid portion 238A of the electromagneticwaveguide system 104B. The output vertical interconnects 138B reside inholes (e.g., 242B) formed by lid wall structures (e.g., 210B) of the lidportion 238A. The output vertical interconnects 138B can mate with(e.g., contact) output plateaus 228C of the example signal board 140A.In some cases, holes of the remaining lid wall structures of the lidportion 238A that are mated with input plateaus 228B of the examplesignal board 140A can be plugged or covered with lid plugs 268.

In some instances, aspects of the signal flow illustrated in FIG. 17Acan be performed by components shown in FIGS. 18A-18C. For example,control signals can be delivered from the input signal processing system128 through the input vertical interconnects 136B to connection inputjunctions on the input plateaus 228B of the example signal board 140A.From the input junctions, the control signals can be communicated intothe electromagnetic waveguide system 104B and routed (e.g.,horizontally) through signal lines 225 (e.g., qubit signal lines 225A orcoupler signal lines 225B) of the signal board 140A to target qubitdevices or coupler devices of the 2D device array 148A. In someinstances, the readout devices (which may be respectively collocatedwith the qubit devices of the 2D device array 148A) produce qubitreadout signals by reflecting or otherwise modulating a readout controlsignal received from the input signal processing system. The qubitreadout signals can be routed (e.g., horizontally) from the readoutdevices through signal lines 225 (e.g., readout signal lines) of theexample signal board 140A to the exterior of the electromagneticwaveguide system 104B. In particular, the qubit readout signals can berouted to connection output junctions on the output plateaus 228C of thesignal board 140A. From the connection output junctions, the qubitreadout signals can be delivered to the output signal processing system130A through the output vertical interconnects 138B.

FIG. 19 shows an example signal routing arrangement 262 for the example2D device array 148A shown in FIGS. 18A-18C. The example routingarrangement 262 can be repeated in space to accommodate larger devicearrays. For example, the attributes of the example routing arrangement262 can be adapted for arrays that include tens or hundreds of qubitdevices organized in N rows and M columns (e.g., where N and M can beequal or unequal), and coupler devices at the bonds between the qubitdevice. For instance, the example routing arrangement 262 can be used ina two-dimensional device array where N=M=4, 16, 32, 64, etc. In thismanner, the example shown in FIG. 19 can be extended to implement QPCsof arbitrarily large size, for example, for general purpose quantumcomputing and quantum information storage.

In the example routing arrangement 262 shown in FIG. 19, each qubitinput plateau 228B-q includes four qubit control ports 156A. Each of thequbit control ports 156A on a qubit input plateau 228B-q is connected(e.g., by a signal line) to a respective one of the four adjacent qubitdevices 144. The four qubit control ports 156A on a qubit input plateau228B-q can contact a qubit input vertical interconnect 136B-q associatedwith the qubit input plateau 228B-q.

In the example routing arrangement 262 shown in FIG. 19, each outputplateau 228C includes four readout control ports 156B. Each of thereadout control ports 156B on an output plateau 228C is connected (e.g.,by a signal line) to a respective one of the four adjacent qubit devices144. The readout qubit control ports 156B on an output plateau 228C cancontact an output vertical interconnect 138B associated with the outputplateau 228C. In some examples, the signal board includes equal numbersof input plateaus 228B-q and output plateaus 228C.

In the example routing arrangement 262 shown in FIG. 19, each couplerinput plateau 228B-c includes four coupler control ports 154A. Each ofthe coupler control ports 154A on a coupler input plateau 228B-c isconnected (e.g., by a signal line) to a respective one of the fouradjacent coupler devices 142. The four coupler control ports 154A on acoupler input plateau 228B-c can contact a coupler input verticalinterconnect 136B-c associated with the coupler input plateau 228B-c. Insome examples, the signal board includes a number of coupler inputplateaus 228B-c that is greater than (e.g., twice) the number of inputplateaus 228B-q or output plateaus 228C.

In the example shown in FIG. 19, rows of alternating qubit inputplateaus 228B-q and coupler input plateaus 228B-c alternate with rows ofalternating output plateaus 228C and coupler input plateaus 228B-c.Similarly, columns of alternating qubit input plateaus 228B-q andcoupler input plateaus 228B-c alternate with columns of alternatingoutput plateaus 228C and coupler input plateaus 228B-c. Thus, there area greater number of input vertical interconnects 136B than outputvertical interconnects 138B. And, among the input vertical interconnects136B, there are a larger number of coupler input vertical interconnects136B-c than qubit input vertical interconnects 136B-q.

In some implementations, groups of input processing hardware components132 of the input signal processing system 128A can be spatiallydistributed (e.g., relative to the QPC 102B) in a manner that shortens(reduces the physical length of) or minimizes the signal paths thatcommunicate between the input processing hardware components and thedevices in the QPC 102B (e.g., qubit devices 144A and coupler devices142A). Similarly, groups of output processing hardware components 134 ofthe output signal processing system 130A can be spatially distributed(e.g., relative to the QPC 102B) in a manner that shortens (reduces thephysical length of) or minimizes the signal paths that communicatebetween the output processing hardware components and the devices in theQPC 102B (e.g., readout devices). Examples of input and output signalprocessing systems that include such groups of input or outputprocessing hardware are described below.

FIG. 20A is a side view of an example system 260A that includes theexample QPC 102B, a modular input signal processing system 128B and amodular output signal processing system 130B. In the example shown, themodular input signal processing system 128B is communicably coupled(e.g., by signal lines) with a signal generator system 120 through inputcontrol system connectors 126C, and is communicably coupled with the QPC102B through QPC input connector hardware 136. Also, the modular outputsignal processing system 130B is communicably coupled with the QPC 102Bthrough QPC output connector hardware 138, and is communicably coupledwith a signal processor system 124 (e.g., by signal lines) throughoutput control system connectors 126D.

As described above in connection with FIGS. 17A-17B, 18A-18C and 19, theexample QPC input connector hardware 136 includes an array of inputvertical interconnects 136B configured to connect with input plateaus ofan example signal board 140A of the QPC 102B. In the example shown inFIG. 20A, the QPC input connector hardware 136 includes, in addition tothe array of input vertical interconnects 136B, an input interconnectplate 135. FIG. 20B shows an example input interconnect plate 135 havingconnectors patterned to match the array of input vertical interconnects136B. Referring again to FIG. 20A, the example input interconnect plate135 is sandwiched between the QPC 102B and the modular input signalprocessing system 128B. In this manner, the example input interconnectplate 135 can couple horizontal control signal lines of the modularinput signal processing system 128B to vertical wires of the inputvertical interconnects 136B.

Also as described above, the QPC output connector hardware 138 includesan array of output vertical interconnects 138B configured to connectwith output plateaus of the example signal board 140A. In the exampleshown in FIG. 20A, the QPC output connector hardware includes, inaddition to the array of output vertical interconnects 138B, an outputinterconnect plate 139. FIG. 20C shows an example output interconnectplate 139 having connectors patterned to match the array of outputvertical interconnects 138B. Referring again to FIG. 20A, the exampleoutput interconnect plate 139 is sandwiched between the QPC 102B and themodular output signal processing system 130B. In this manner, theexample output interconnect plate 139 can couple vertical wires of theoutput vertical interconnects 138B to horizontal signal lines of themodular output signal processing system 130B.

FIG. 20D is a perspective view of the example modular input signalprocessing system 128B. The modular input signal processing system 128Bcan include M input modules, where each input module 268-k (k=1 M)includes a respective subset of input control system connectors 126C andinput processing hardware 132A. Each input module 268-k is configured todeliver control signals to qubit devices and coupler devices arranged ina k^(th) section of the 2D device array 148A of the QPC 102B. In someimplementations, the sections are defined based on a number of rows ineach section. For example, each section may include N/M rows, where N isthe total number of rows of the 2D device array 148A. In otherimplementations, the sections are defined based on a number of columnsin each section. For example, each section may include N/M columns,where N is the total number of columns of the 2D device array 148A. Insome other implementations, the sections are defined based on otherschemes. In the example illustrated in FIG. 20D, each quadrant of the 2Ddevice array can be a section that is controlled by a respective inputmodule 268-k. The sections of a device array may be arranged in anothermanner.

In some implementations, the input modules 268-k of the example modularinput signal processing system 128B each include input processing cardshoused on an input processing board 270A. The example input processingboard 270A can include receptacle slots that support the inputprocessing cards, and allow the input processing cards to be removed orexchanged for other components. Here, each of the receptacle slots thatsupports a respective input processing card is located on the inputprocessing board 270A adjacent to the corresponding section of the QPC102B. In the example input processing board 270A shown in FIG. 20D, theinput processing cards in the input module 268-k are located on theinput processing board 270A adjacent to the k^(th) quadrant of the QPC102B. Signal lines that carry control signals for respective qubitdevices or coupler devices arranged in the k^(th) section of the QPC102B are routed from the receptacle slot that supports the inputprocessing cards in the input module 268-k to an adjacent k^(th) portionof the input interconnect plate 135. The signal lines and processingcards can be arranged in an efficient manner, for example, in a mannerthat reduces or minimizes a length of the signal lines in the inputprocessing board 270A.

In some implementations, the input modules 268-k of the example modularinput signal processing system 128B are formed on respective inputprocessing board sections of the input processing board 270A. In suchcases, each of the input processing board sections is located on theinput processing board 270A adjacent to the k^(th) section of the QPC102B. In the example input processing board 270A shown in FIG. 20D, theinput processing board section for the input module 268-k is located onthe input processing board 270A adjacent to the k^(th) quadrant of theQPC 102B.

In the example modular input signal processing system 128B, the inputprocessing hardware 132A of each input module 268-k can include one ormore de-multiplexer circuits. In some implementations, the receivedcontrol signals targeted for a subgroup of qubit devices or couplerdevices of the k^(th) quadrant are multiplexed together. In someimplementations, the received control signals targeted for a subgroup ofqubit devices and coupler devices arranged in the k^(th) quadrant aremultiplexed on a single input channel. In some implementations, writesignals and read signals targeted for a qubit device arranged in thek^(th) quadrant are multiplexed on a single input channel. Thede-multiplexer circuits of the input module 268-k can be configured toseparate the multiplexed control signals, for example, device-by-device.

The example input processing hardware 132A of each input module 268-kcan include bias processing circuits. The bias processing circuits ofthe input module 268-k are configured to combine AC control signals withDC bias control signals targeted for a coupler device of the k^(th)quadrant. These and other input processing hardware 132A of each inputmodule 268-k of the example modular input signal processing system 128Bare described in more detail below in connection with FIG. 23A andothers.

Furthermore, the subset of input control system connectors 126C of eachinput module 268-k is configured to receive, from the signal generatorsystem 120, the above-noted multiplexed control signals for qubitdevices and coupler devices of the k^(th) quadrant of the 2D devicearray 148A. The multiplexed signals can be delivered from the subset ofinput control system connectors 126C of input module 268-k to the inputprocessing hardware 132A thereof through signal lines routed on orthrough the input processing board 270A.

FIG. 20E is a perspective view of the example modular output signalprocessing system 130B. The modular output signal processing system 130Bcan include M output modules, where each output module 272-k (k=1 M)includes a respective subset of output control system connectors 126Dand output processing hardware 134A. Each output module 272-k isconfigured to receive readout signals from readout devices collocatedwith qubit devices arranged in a k^(th) section of the 2D device array148A of the QPC 102B. The sections of the 2D device array 148A can beallocated in the same manner as the sections are allocated for controlsignal management, or in a different manner. In the example illustratedin FIG. 20E, each quadrant of the 2D device array can be a section thatsends readout signals to a respective output module 272-k.

In some implementations, the output modules 272-k of the example modularoutput signal processing system 130B each include output processingcards housed on an output processing board 270B. The example outputprocessing board 270B can include receptacle slots that support theoutput processing cards, and allow the output processing cards to beremoved or exchanged for other components. Here, each of the receptacleslots that supports a respective output processing card is located onthe output processing board 270B adjacent to the corresponding sectionof the QPC 102B. In the example output processing board 270B shown inFIG. 20E, the output processing cards in the output module 272-k arelocated on the output processing board 270B adjacent to the k^(th)quadrant of the QPC 102B. Signal lines that carry readout signals fromreadout devices in the k^(th) section are routed from the receptacleslot that supports the output processing card 272-k to adjacent k^(th)portion of the output interconnect plate 139. The signal lines andprocessing cards can be arranged in an efficient manner, for example, ina manner that reduces or minimizes a length of the signal lines in theoutput processing board 270B.

In some implementations, the output modules of the example modularoutput signal processing system 130B are formed on respective outputprocessing board sections of an output processing board 270B. In suchcases, each of the output processing board sections can be located onthe output processing board 270B adjacent to the k^(th) section of theQPC 102B. In the example output processing board 270B shown in FIG. 20E,the output processing board section for the output module 272-k islocated on the output processing board 270B adjacent to the k^(th)quadrant of the QPC 102B.

In the example modular output signal processing system 130B, the outputprocessing hardware 134A of each output module 272-k can includeisolator circuits. When p is the number of qubit devices arranged in thek^(th) section of the QPC 102B associated with the output module 272-k,the isolator circuits of the output module 272-k can be configured toisolate respective p readout signals received from readout devicesarranged in the k^(th) section.

The example output processing hardware 134A of each output module 272-kcan include parametric amplifier circuits and their respective pump ordriver circuits. The parametric amplifier circuits can be configured toamplify, in conjunction with the pump circuits, the isolated p readoutsignals. In this manner, the readout signals received from readoutdevices arranged in the k^(th) section can be amplified at a locationadjacent to the k^(th) section of the QPC 102B where the readout signalswere generated. Amplifying or otherwise processing readout signals nearthe QPC 102B can reduce noise, e.g., transmission line noise or otherenvironmental noise sources.

The example output processing hardware 134A of each output module 272-kcan include one or more multiplexer circuits. The multiplexer circuitsof the output module 272-k can be configured to combine the p amplifiedreadout signals corresponding to the p qubit devices of the k^(th)section into a k^(th) modulated readout signal associated with thek^(th) section. These and other output processing hardware 134A of eachoutput module 272-k of the example modular output signal processingsystem 130B are described in more detail below in connection with FIG.23A and others. Other configurations of the processing cards can be usedin an output signal processing system or an input signal processingsystem.

Additionally, the subset of output control system connectors 126D ofeach output module 272-k can be configured to receive, from themultiplexer circuits of output module 272-k, the k^(th) multiplexedreadout signal. The k^(th) multiplexed readout signal can be deliveredfrom the multiplexer circuits of output module 272-k to its subset ofoutput control system connectors 126D through a signal line routed on orthrough the output processing board 270B. The k^(th) multiplexed readoutsignal can be extracted from the example modular output signalprocessing system 130B at the subset of output control system connectors126D for the output module 272-k. The extracted multiplexed readoutsignal can be delivered to a signal processing system 124.

FIGS. 21A-21C are diagrams showing example operating frequencies fordevices in a quantum processor cell. In some instances, the operatingfrequencies and other attributes shown and described with respect toFIGS. 21A-21C can implemented by the example quantum processor cells102A, 102B, 102C described above, or another type of quantum processorcell. FIG. 21A shows a frequency spectrum plot 2100 that indicatesexample operating frequencies of qubit devices and readout devices. Asshown in FIG. 21A, the frequency spectrum plot 2100 includes frequenciesranging from 3.2 GHz to 4.1 GHz. The example operating frequencies andother attributes shown in FIG. 21A can be adapted to other frequencybands or scaled to other frequency units, for example, for use withdevices or systems operating in other frequency ranges.

The example frequency spectrum plot 2100 in FIG. 21A indicates fivedistinct qubit operating frequencies and five distinct readoutfrequencies. In some cases, another number of qubit operatingfrequencies and readout frequencies can be used. For example, FIGS.22A-C show an example where six qubit operating frequencies and sixreadout frequencies are used.

In the example shown in FIG. 21A, a first qubit operating frequency2101A and a first readout frequency 2102A are within a first frequencyband at 3.2 GHz, and the first qubit operating frequency 2101A is lessthan the first readout frequency 2102A; a second qubit operatingfrequency 2101B and a second readout frequency 2102B are within a secondfrequency band at 3.6 GHz, and the second qubit operating frequency2101B is less than the second readout frequency 2102B; a third qubitoperating frequency 2101C and a third readout frequency 2102C are withina third frequency band at 3.8 GHz, and the third qubit operatingfrequency 2101C is less than the third readout frequency 2102C; a fourthqubit operating frequency 2101D and a fourth readout frequency 2102D arewithin a fourth frequency band at 3.9 GHz, and the fourth qubitoperating frequency 2101D is less than the fourth readout frequency2102D; a fifth qubit operating frequency 2101E and a fifth readoutfrequency 2102E are within a fifth frequency band at 4.1 GHz, and thefifth qubit operating frequency 2101E is less than the fifth readoutfrequency 2102E. Each of the respective frequency bands is separate anddistinct from the other frequency bands, so that there is no overlapbetween any two frequency bands indicated in the frequency spectrum plot2100.

In the example shown, the respective readout frequencies are interleavedwith the qubit operating frequencies in the frequency spectrum plot2100. For example, progressing from the low end to the high end of thefrequency spectrum, the qubit operating frequencies alternate with thereadout frequencies. In some instances, the qubit operating frequencyand the readout frequency within each frequency band can be interchangedor otherwise modified (increased or decreased), such that the qubitoperating frequency may be higher than the readout frequency within oneor more of the frequency bands. In some implementations, the qubitoperating frequencies are not interleaved with the readout frequencies;for example, the qubit operating frequencies can be grouped in onefrequency band, and the readout frequencies can be grouped in aseparate, distinct frequency band.

As shown in FIG. 21A, the frequency bands are spaced apart from eachother by intervals in the frequency spectrum 2100. The intervals betweenthe neighboring pairs of frequency bands vary. For example, the intervalbetween the first frequency band and the second frequency band is 0.4GHz, and the interval between the second frequency band and the thirdfrequency band is 0.2 GHz. Thus, the second frequency band is spacedapart from one of its nearest-neighbor frequency bands by a firstinterval (0.4 GHz), and the second frequency band is spaced apart fromits other nearest-neighbor frequency band by a second, distinct interval(0.2 GHz). Some of the intervals between nearest-neighbor frequencybands are equal. For example, the spacing between the second frequencyband and the third frequency band is 0.2 GHz, and the spacing betweenthe fourth frequency band at the fifth frequency band is also 0.2 GHz.Thus, the intervals shown in the frequency spectrum plot 2100 can besorted into subsets of equal intervals (where the intervals that formeach subset are equal to each other, and intervals that are in distinctsubsets are unequal).

FIG. 21B shows a frequency difference plot that indicates differencesbetween the operating frequencies shown in FIG. 21A, and frequencydifferences for nearest neighbor qubits in the device array 2120 in FIG.21C. In particular, each horizontal line indicates the frequencydifference between two of the frequency bands in FIG. 21A. For example,the frequency difference 2105A indicates the difference between thefirst frequency band in FIG. 21A (which includes the first qubitoperating frequency 2101A and the first readout frequency 2102A) and thesecond frequency band (which includes the second qubit operatingfrequency 2101B and the second readout operating frequency 2102B).Similarly, the frequency difference 2105B indicates the frequencydifference between the first frequency band and the third frequency band(which includes the third qubit operating frequency 2101C and the thirdreadout frequency 2102C).

In some instances, the frequency differences shown in FIG. 21B can beused to operate coupler devices in a quantum processor cell. Forinstance, the frequency differences indicated in the frequencydifference plot 2110 can be used as drive frequencies for couplerdevices that interact with qubit devices having the qubit operatingfrequencies indicated in FIG. 21A. In some implementations, couplerdevices can be operated using the sum frequencies of the qubitfrequencies, rather than difference frequencies.

FIG. 21C shows an example arrangement of devices in an example devicearray 2120. The circles in the device array 2120 indicate the locationsof qubit devices, and the lines between the circles indicate thelocations of coupler devices. FIG. 21C also indicates the locations ofplateaus in the device array 2120 where signals are communicated betweenan external control system and the devices in the device array 2120. Asshown in FIG. 21C, the frequency difference between any given qubit andeach of its nearest-neighbor qubits is distinct. A device array mayinclude additional or different features, and the devices and otherattributes may be arranged in another manner.

In the example device array 2120, the qubit devices have respectivequbit operating frequencies that are indicated by the shading of thequbit devices in the figure. For example, the first qubit device 2121Ahas an operating frequency that corresponds to the first qubit operatingfrequency 2101A shown in FIG. 21A, the qubit device 2121B has anoperating frequency that corresponds to the second qubit operatingfrequency 2101B shown in FIG. 21A, etc.

The device array 2120 shown in FIG. 21C is an example of amulti-dimensional array that includes groups of qubit devices. In theexample shown in FIG. 21C, each group of qubit devices includes fivequbit devices, and the qubit devices in each group have distinctoperating frequencies (corresponding to the five distinct qubitoperating frequencies 2101A, 2101B, 2101C, 2101D, 2101E indicated inFIG. 21A). Thus, in the example shown, no two qubit devices in a grouphave the same qubit operating frequency, and the qubit control signalsfor the qubit devices in each group can be communicated on a singlephysical channel using, for example, the multiplexing andde-multiplexing systems and techniques described in this document. Forexample, each qubit device in the group of five qubit devices 2121A,2121B, 2121C, 2121D, 2121E has a distinct qubit operating frequency, andqubit control signals addressed to the group of five qubit devices canbe multiplexed onto a common signal line.

In FIG. 21C, the operating frequency of each individual coupler devicecan be selected based on the operating frequencies of the two qubitdevices that are coupled by the individual coupler device. For example,the coupler device residing at the interval between the first qubitdevice 2121A and the third qubit device 2121C can be driven at a drivefrequency that corresponds to the frequency difference 2105B shown inFIG. 21B, which is the difference between the first qubit operatingfrequency 2101A and the third qubit operating frequency 2101C; and thecoupler device residing at the interval between the first qubit device2121A and the fourth qubit device 2121D can be driven at a drivefrequency that corresponds to the difference between the first qubitoperating frequency 2101A and the fourth qubit operating frequency2101D.

The example device array 2120 includes readout devices associated withthe qubit devices. Each readout device can be operably coupled to asingle, respective qubit device and configured to produce a qubitreadout signal that indicates the quantum state of the single,respective qubit device. In the example shown, the readout device thatis configured to read qubit device 2121A operates at the first readoutfrequency 2102A shown in FIG. 21A, the readout device that is configuredto readout qubit device 2121B operates at the second readout frequency2102B shown in FIG. 21A, etc.

In some implementations, the example device array 2120 includes groupsof readout devices that correspond to the groups of qubit devices. Forexample, a group of five readout devices can be associated with thegroup of five qubit devices 2121A, 2121B, 2121C, 2121D, 2121E, and eachreadout device in the group can be operatively coupled to a respectiveone of the qubit devices. Like the groups of qubit devices, the readoutdevices within each group have distinct operating frequencies thatcorrespond to the readout frequencies shown in FIG. 21A. In particular,each group of readout devices includes five readout devices, and thereadout devices in each group have distinct readout frequencies(corresponding to the five distinct readout frequencies 2102A, 2102B,2102C, 2102D, 2102E indicated in FIG. 21A). In some cases, each groupcan include another number of devices (e.g., a group may include two,three, four, five, six, seven, eight, nine, ten, or more devices).

The example device array 2120 includes three types of plateaus. A firstsubset of the plateaus include signal lines that deliver qubit controlsignals to the qubit devices, a second subset of the plateaus includesignal lines that deliver coupler control signals to the controldevices, and a third subset of the plateaus include signal lines thatreceive qubit readout signals from the readout devices. In the exampleshown in FIG. 21C, the qubit control plateau 2123 communicates qubitcontrol signals to the four surrounding qubit devices (2121A, 2121C,2121D, 2121E). Similarly, the coupler control plateau 2124 communicatescoupler control signals to the four surrounding coupler devices (thecoupler device between the qubits 2121D and 2121E, the coupler devicebetween the qubits 2121D and 2121B, and the two other adjacent couplerdevices). The qubit readout plateau 2125 communicates qubit readoutsignals from the four surrounding readout devices (including the readoutdevice associated with the qubit device 2121E, and the three otheradjacent readout devices). Additional or different types of plateaus maybe used, and the plateaus may be arranged as shown or in another manner.

In some instances, the qubit devices in the device array 2120 receivequbit control signals that are configured to manipulate the quantumstate of the qubit devices. For example, the qubit control signal cancorrespond to an encoding operation or a single-qubit gate in a quantumalgorithm, a quantum error correction procedure, a quantum statedistillation procedure, etc. In the example shown, the qubit controlsignals are microwave pulses, at the qubit operating frequenciesindicated in FIG. 21A. In some cases, other types of qubit controlsignals may be used.

In some instances, qubit control signals for a group of qubits can becommunicated (e.g., from a signal generator system) on a single physicalchannel to an input signal processing system associated with the devicearray 2120. The input signal processing system can separate the qubitcontrol signals for each individual qubit device in the group based onthe frequencies of the respective qubit control signals. For example,the qubit control signals that are addressed to the qubit device 2121Acan have a signal frequency that corresponds to the qubit operatingfrequency 2101A, which can be separated (e.g., by operation of ade-multiplexer) from qubit control signals in other frequency ranges.Once the qubit control signals are divided onto separate physicalchannels, the qubit control signals can be routed to the appropriatequbit device and delivered through the appropriate qubit controlplateau.

In some instances, the readout devices in the device array 2120 producequbit readout signals based on the quantum states of the qubit devices.In some instances, the readout devices produce qubit readout signals inresponse to readout control signals received by the respective readoutdevices, for example, by reflecting the readout control signals withadditional information (e.g., a phase shift, a frequency shift, anamplitude shift, etc.) that indicates the state of a qubit device. Thequbit readout signals can be produced by the readout devices in responseto the readout control signals, for example, based on electromagneticinteractions between the individual readout device and its respectivequbit device. The qubit readout signals produced by a group of readoutdevices can be combined (e.g., multiplexed) onto a single physicalchannel. For example, the qubit readout signals can be communicated fromthe respective readout devices through the appropriate qubit readoutplateaus to an output signal processing system. The output signalprocessing system can receive the respective qubit readout signals onmultiple distinct physical channels and multiplex them onto a singlephysical channel.

The example device array 2120 is an example of a multi-dimensional arrayof qubit devices that includes sub-arrays, where each sub-array isassociated with a separate one of the frequency bands shown in FIG. 21A.Each group of qubit devices includes one qubit device in each of thesub-arrays. In particular, the example device array 2120 includes fivedistinct sub-arrays, one sub-array for each frequency band shown in FIG.21A. For example, all of the qubit devices in the example device array2120 that are shaded as the first qubit device 2121A form a firstsub-array, such that all qubit devices in the first sub-array have thefirst qubit operating frequency 2101A shown in FIG. 21A. Similarly, allof the qubit devices in the example device array 2120 that are shaded asthe second qubit device 212B form a second sub-array, such that allqubit devices in the second sub-array have the second qubit operatingfrequency 2101B shown in FIG. 21A. In the example shown, the sub-arraysare mutually exclusive, such that no qubit device is included in morethan one sub-array. Also in the example shown, the sub-arrays fullycover the device array 2120, such that every qubit device is included inone of the sub-arrays.

As shown in FIG. 21C, the qubit devices collectively define a tilingover the multi-dimensional device array 2120. In the example shown, eachtile in the tiling is five-by-five in size; an individual tile 2140 isindicated by the dashed outline in FIG. 21C. The device array 2120 caninclude multiple tiles each arranged as the example tile 2140. The tilesin a multi-dimensional array can be repeated in any direction to scalethe device array 2120 to include more qubit devices.

The example two-dimensional device array 2120 shown in FIG. 21C is anexample of a rectilinear array, in which the qubit devices are arrangedin rows and columns, with the columns perpendicular to the rows. Theexample two-dimensional array shown in FIG. 21C is also an example of asquare array, in which the spacing is equal between all rectilinear rowsand columns, and therefore, the physical length spacing is equal betweeneach pair of nearest-neighbor qubit devices. In some examples, thephysical length spacing between each pair of nearest-neighbor qubitdevices is in the range of 0.2 to 2.0 centimeters. Another type ofmulti-dimensional array can be used, and the device spacing can be in adifferent range. For example, the array can be non-rectilinear, suchthat the rows are not perpendicular to the columns, or the array can berectangular, such that the rows are spaced differently than the columns.Other types of two-dimensional arrays may be formed. In some instances,the example two-dimensional device array 2120 can be extended to threedimensions.

As shown in FIG. 21C, each of the qubit devices has two or morenearest-neighbor qubit devices. Thus, each qubit device is a member ofat least two pairs of nearest-neighbor qubits. The qubit devices in eachpair of nearest-neighbor qubit devices are connected to each other by aline (which represents the location of a coupler device) in the diagramshown in FIG. 21C. The four qubit devices at the corners of the devicearray 2120 each have two nearest-neighbors, the five qubit devices alongeach edge (between the corners) of the device array 2120 each have threenearest-neighbors, and the internal qubit devices that are not along theedges or corners each have four nearest-neighbors. In an examplethree-dimensional rectilinear array, the qubit devices at the cornerswould each have three nearest-neighbors, the qubit devices along eachedge between the corners would each have four nearest-neighbors, and theinternal qubit devices that are not along the edges or corners wouldeach have six nearest-neighbors. Other types of three-dimensional arraysand lattices may be used. For instance, the devices can be arranged toform a Bravais lattice.

As shown in FIG. 21C, the qubit operating frequency of each qubit deviceis distinct from the qubit operating frequency of each of itsnearest-neighbor qubit devices. For example, the qubit device 2121E hasthe fifth qubit operating frequency 2101E shown in FIG. 21A, and none ofits nearest-neighbor qubit devices has the fifth qubit operatingfrequency 2101E. In particular, the nearest-neighbors of the qubitdevice 2121E have the first qubit operating frequency 2101A, the secondqubit operating frequency 2101B, the third qubit operating frequency2101C, and the fourth qubit operating frequency 2101D.

In the example shown in FIG. 21C, the readout frequencies of the readoutdevices in the device array 2120 can be arranged according to the samepattern as the qubit operating frequencies. Thus, the readout frequencyof each readout device in the device array 2120 can be distinct from thereadout frequency of each of its nearest-neighbor readout devices. Forexample, the readout device associated with the qubit device 2121E hasthe fifth readout frequency 2102E shown in FIG. 21A, and none of itsnearest-neighbor readout devices has the readout frequency 2102E. Inparticular, the nearest-neighbors of the readout device associated withthe qubit device 2121E have the first readout frequency 2102A, thesecond readout frequency 2102B, the third readout frequency 2102C, andthe fourth readout frequency 2102D. Other arrangements of readoutfrequencies may be used.

For the example gate scheme shown in FIGS. 4C-4E or other gate schemes,the coupler devices in the example device array 2120 can be arrangedsuch that no two coupler devices that have the same drive frequency arecoupled to the same qubit device. For example, the coupler devicebetween the qubit devices 2121D and 2121E can be driven at or near adrive frequency that is the difference between the operating frequenciesof the qubit devices 2121D and 2121E. In particular, the coupler devicebetween the qubit devices 2121D and 2121E can operate at 0.2 GHz, whichis the difference between the fourth qubit operating frequency 2101D andthe fifth qubit operating frequency 2101E. The other three couplerdevices that are adjacent to the qubit device 2121E operate at differentdrive frequencies (i.e., different from 0.2 GHz). Specifically, thethree other coupler devices that are adjacent to the qubit device 2121Eare driven at 0.3 GHz (the difference between the third qubit operatingfrequency 2101C and the fifth qubit operating frequency 2101E), 0.9 GHz(the difference between the first qubit operating frequency 2101A andthe fifth qubit operating frequency 2101E), and 0.5 GHz (the differencebetween the second qubit operating frequency 2101B and the fifth qubitoperating frequency 2101E).

FIGS. 22A-22C are diagrams showing example operating frequencies fordevices in a quantum processor cell. The example operating frequenciesshown in FIGS. 22A-22C represent an alternative to the example shown inFIGS. 21A-21C. In some instances, the example operating frequenciesshown in FIGS. 22A-22C can be implemented by a quantum processor cell ina manner that is analogous to the manner described with respect to FIGS.21A-C. For instance, the operating frequencies and other attributesshown and described with respect to FIGS. 22A-C can be implemented bythe example quantum processor cells 102A, 102B, 102C described above oranother type of quantum processor cell.

FIG. 22A shows a frequency spectrum plot 2200 that indicates exampleoperating frequencies of qubit devices and readout devices. As shown inFIG. 22A, the frequency spectrum includes frequencies ranging from 3.2GHz to 3.9 GHz. The example operating frequencies shown in FIG. 22A canbe adapted to other frequency bands or scaled to other frequency units,for example, for use with devices operating in other frequency ranges.

The example frequency spectrum plot 2200 in FIG. 22A indicates sixdistinct operating frequency bands 2201A, 2201B, 2201C, 2201D, 2201E and2201F. Qubit operating frequencies and readout frequencies can beselected in each of the respective frequency bands. For example, eachfrequency band can include a qubit operating frequency and a readoutfrequency, such that there are six distinct qubit operating frequenciesand six distinct readout frequencies. As shown in FIG. 22A, thefrequency bands are spaced apart from each other at intervals along thefrequency spectrum plot 2200, and the intervals between the neighboringpairs of frequency bands vary. Moreover, the frequency spectrum plot2200 indicates two subsets of intervals, where the intervals within eachsubset are equal to each other (either 0.1 GHz or 0.2 GHz), anddifferent from the intervals in the other subsets.

FIG. 22B shows a frequency difference plot that indicates differencesbetween the frequency bands shown in FIG. 22B. In particular, eachhorizontal line indicates the frequency difference between two of thefrequency bands and FIG. 22B. For example, the frequency difference2205A indicates the difference between the second frequency band 2201Band the third frequency band 2201C. Similarly, the frequency difference2205B indicates the difference between the second frequency band 2201Band the fourth frequency band 2201D, and the frequency difference 2205Cindicates the difference between the third frequency band 2201C and thesixth frequency band 2201F. In the example shown, the frequencydifferences shown in FIG. 22B can be used to operate coupler devices ina quantum processor cell. As described with respect to FIG. 22C, thefrequency differences indicated in the frequency difference plot 2210can be used as drive frequencies for coupler devices that interact withqubit devices having the qubit operating frequencies indicated in FIG.22A.

FIG. 22C shows an example arrangement of device frequencies in a devicearray 2220. Similar to FIG. 21C, the circles in the two-dimensionaldevice array 2220 shown in FIG. 22C indicate the locations of qubitdevices. The shading of each circle indicates the qubit operatingfrequency of the respective qubit device. For instance, the qubit device2221A has a qubit operating frequency in the first frequency band 2201Ashown in FIG. 22A, the qubit device 2221B has a qubit operatingfrequency in the second frequency band 2201B shown in FIG. 22A, etc.

Similar to FIG. 21C, the lines between the circles in thetwo-dimensional device array 2220 shown in FIG. 22C indicate thelocations of coupler devices. The integer beside each line indicates thedrive frequency that is used to operate the respective coupler device.For instance, the coupler device 2230B (which resides at the intervalbetween the qubit device 2221B and the qubit device 2221D) is labeled“3” and is driven at a frequency of 0.3 GHz to produce an interactionbetween the two neighboring qubit devices (2221B, 2221D); the couplerdevice 2230A (which resides at the interval between the qubit device2221B and the qubit device 2221C) is labeled “2” and is driven at afrequency of 0.2 GHz to produce an interaction between the twoneighboring qubit devices (2221B, 2221C); and the coupler device 2230C(which resides at the interval between the qubit device 2221C and thequbit device 2221F) is labeled “4” and is driven at a frequency of 0.4GHz to produce an interaction between the two neighboring qubit devices(2221C, 2221F).

The example device array 2220 includes groups of qubit devices andgroups of readout devices. The groups of devices in the device array2220 in FIG. 22C are similar to the groups in the example device array2120 in FIG. 21C. For instance, no two qubit devices in a group have thesame qubit operating frequency, and the control signals for the qubitdevices in each group can be communicated on a single physical channel.However, the groups in the device array 2220 each include six devices(according to the six frequency bands shown in the frequency spectrumplot 2200) whereas the groups in the device array 2120 each include fivedevices (according to the five frequency bands shown in the frequencyspectrum plot 2100). As an example, the qubit devices 2221A, 2221B,2221C, 2221D, 2221E and 2221F all have distinct qubit operatingfrequencies and form a group in the example device array 2220.Accordingly, the multi-dimensional device array shown in FIG. 22Cincludes six distinct sub-arrays, one sub-array for each of thefrequency bands.

In the example shown in FIG. 22C, the qubit devices collectively definea tiling over the multi-dimensional device array 2220. In the exampleshown in FIG. 22C, each tile in the tiling is six-by-six in size; anindividual tile 2240 is indicated by the dashed outline in FIG. 22C. Thedevice array 2220 can include multiple tiles each arranged as theexample tile 2240. The tiles in the multi-dimensional array can berepeated in any direction to scale the device array 2220 to include morequbit devices.

The device array 2220 in FIG. 22C is another example of atwo-dimensional square array, where each of the qubit devices has two ormore nearest-neighbor qubit devices. Each pair of nearest-neighbor qubitdevices is connected by a line (which represents the location of acoupler device) in the diagram shown in FIG. 22C. As shown in FIG. 22C,the qubit operating frequency of each qubit device is distinct from thequbit operating frequency of each of its nearest-neighbor qubit devices.Moreover, the readout frequencies of the readout devices in the devicearray 2220 can be arranged according to the same pattern as the qubitoperating frequencies. As shown, the coupler devices in the device array2220 are arranged such that no two coupler devices that have the samedrive frequency are coupled to the same qubit device. Readout devices inthe device array 2220 can each be coupled to a single, respective qubitdevice and configured to produce a qubit readout signal that indicates aquantum state of the respective qubit device.

In the example shown in FIG. 22C, the multi-dimensional array definesintervals between the qubit devices, and the coupler devices reside atthe intervals between the neighboring pairs of the qubit devices in themulti-dimensional array. A first subset of the intervals are definedalong the rows of the array, and a second subset of the intervals aredefined along the columns of the array. Each coupler device isconfigured to generate an electromagnetic interaction between therespective neighboring pair of qubit devices that the coupler deviceresides between.

In some implementations, each of the coupler devices receives couplercontrol signals that are configured to produce an electromagneticinteraction between its neighboring pair of qubit devices (the pair ofqubit devices that the coupler device resides between). For instance,the coupler control signals can be configured to produce a first-orderinteraction between the neighboring pair of qubit devices, and theinteraction can modulate the degree of quantum entanglement of the qubitdevices. In some cases, the coupler control signal corresponds to atwo-qubit gate used in the execution of a quantum algorithm. In theexample shown, the coupler control signals are radio frequency ormicrowave frequency pulses, at the drive frequencies indicated in FIG.22B. In some cases, other types of coupler control signals may be used.

In some instances, each of the coupler devices is operated by applyingboth an offset field (e.g., a DC component) and a drive field (e.g., anAC component), while each qubit device is operated by applying only adrive field without an offset field. For example, the coupler devicescan be implemented as flux qubit devices, and the qubit devices can beimplemented as charge qubit devices. In some instances, each of thecoupler devices has a respective coupler operating frequency that varieswith an offset electromagnetic field experienced by the coupler device,and each qubit device has a respective qubit operating frequency that isindependent of the electromagnetic field experienced by the qubitdevice. For example, the coupler devices can be implemented as fluxoniumdevices, and the qubit devices can be implemented as transmon devices.

In some implementations, each coupler device includes an offset fieldgenerator (e.g., an inductor) that is configured to generate an offsetfield that tunes the coupler operating frequency of the coupler device.The coupler device may also include a resonant circuit that isconfigured to generate an electromagnetic interaction between theneighboring pair of qubit devices. The coupler control signals receivedby the coupler device can include a DC component that causes the offsetfield generator of the coupler device to produce an offsetelectromagnetic field. The offset electromagnetic field can tune thecoupler device to a particular frequency that increases a rate ofinteraction between the neighboring pair of qubit devices. The couplercontrol signals can also include an AC component that drives theresonant circuit at a drive frequency that corresponds to the differencebetween or sum of the qubit operating frequencies of the neighboringqubit devices. For instance, the AC component of the coupler controlsignals can have a frequency that is configured according to the integerbeside the respective coupler device in FIG. 22C. In the example shown,the AC component of each coupler control signal is a radio frequency ormicrowave pulse.

In some implementations, the example arrangements of qubit operatingfrequencies and coupler drive frequencies shown in FIGS. 21C and 22C canprovide advantages for building and operating a quantum computingsystem. For instance, the frequency allocation may allow the fullspectrum of operating frequencies to be generated on a single channeland communicated in an efficient manner. This may reduce the number ofwires and electronic components, the cost of materials, construction andmaintenance, and provide other efficiencies. As another example, thearrangement of operating frequencies can enable scaling to largernumbers of qubits, by providing a repeatable pattern of operatingfrequencies. For example, each tile can use the same frequency spectrumas the example tiles 2140, 2240, or another tiling may be used.

The example device arrays 2120 and 2220 can form part of the examplequantum processor cell 102A shown in FIG. 2, or the device arrays 2120,2220 can be implemented in another type of quantum computing system. Insome instances, the example device arrays 2120, 2220 can be operatedbased on the operating techniques and hardware shown in FIG. 23A, or thedevice array can be operated using other types of techniques or othertypes of hardware. In some cases, the qubit devices, readout devices,and coupler devices in the example device arrays 2120, 2220 are housedin the electromagnetic waveguide system 104 shown in FIG. 2 (e.g., inthe type of arrangement shown in FIG. 5A), or the devices can be housedin another type of environment. Moreover, the qubit devices, readoutdevices and coupler devices in the example arrays 2120, 2220 can beimplemented according to the examples shown in FIGS. 3A-3E, and they mayoperate as described, for example, with respect to FIGS. 4A, 4B, 4C, 4Dand 4E. Alternatively, the devices can be implemented according to otherdesigns or they may operate in another manner.

FIG. 23A is a block diagram of an example quantum computing system 2300.The example quantum computing system 2300 can include the features ofthe example quantum computing system 100A shown in FIG. 2, or theexample quantum computing system 2300 can be implemented in anothermanner. As shown in FIG. 23A, the example quantum computing system 2300includes control system components that operate in a room temperaturestage 2301. The room temperature stage 2301 can include operatingconditions and an operational environment that is consistent withstandard temperature and pressure, or another type of room temperatureenvironment. For example, the components that operate in the roomtemperature stage 2301 can operate around 300 Kelvin or another typicalroom temperature.

The example quantum computing system 2300 also includes signal deliveryand quantum processor cell components that operate in a cryogenictemperature stage 2331. The cryogenic temperature stage 2331 can includeoperating conditions and an operational environment that is consistentwith cryogenic conditions. For example, the components that operate inthe cryogenic temperature stage 2331 can operate at 5-10 mK or anothercryogenic temperature. In some cases, the cryogenic temperature stage2331 can provide appropriate operating conditions for low-temperaturesuperconducting materials. In some cases, the cryogenic temperaturestage 2331 includes an ultra-low noise environment that is shieldedagainst an external environment. For example, the example quantumcomputing system can include a shielding system or shielding materialsthat prevent unwanted radio waves, microwaves or optical signals, orunwanted magnetic fields or mechanical vibrations, from entering theoperating the environment of the cryogenic temperature stage 2331. Forinstance the shielding materials may include metallic, superconductingor lossy materials.

The example quantum computing system 2300 also includes components thatoperate in one or more intermediate temperature stages 2321. Theintermediate temperature stages 2321 can include operating conditionsand an operational environment that provide a buffer between the roomtemperature stage 2301 and the cryogenic temperature stage 2331. Theintermediate temperature stages 2321 may be shielded from each other orfrom the room temperature stage 2301, for example, to maintain atemperature or noise level in the operating environment of theintermediate temperature stages 2321.

Signals can be communicated between the components operating in thedifferent temperature stages of the quantum computing system 2300. Insome cases, analog control signals are communicated in the roomtemperature environment on coaxial cables, waveguides, high-densitymicrowave wires, or other types of transmission lines, and the analogcontrol signals can be transferred between the room temperatureenvironment and the intermediate temperature environments usingfeedthrough devices that allow signals to pass through but provideisolation for spurious electromagnetic noise outside of the signal band(e.g., light-tight feedthrough devices). In some cases, analog controlsignals are communicated in the cryogenic temperature environment onsuperconducting high-density microwave wires, co-axial or co-planarwaveguide structures, or other types of transmission lines, and analogcontrol signals can be transferred between the cryogenic temperatureenvironment and the intermediate temperature environments usingfeedthrough devices (e.g., light-tight feedthrough devices).

The example quantum computing system 2300 includes multiple operatingdomains. Each of the operating domains can include dedicated hardware atone or more stages of the quantum computing system 2300. The operatingdomains can be controlled collectively and may share hardware at one ofmore stages of the quantum computing system 2300. In the example shownin FIG. 23A, the quantum processor includes an array of qubit devices,and each operating domain includes a particular group of the qubitdevices and the associated devices and other hardware that operate inconnection with the particular group of qubit devices. The devices ineach group have distinct operating frequencies, such as, for example,the groups of devices described with respect to FIGS. 21A-C and 22A-C. Adevice in one group can have the same operating frequency as a deviceand another group, since the groups operate within different operatingdomains.

In some implementations, the qubit operating frequencies for anoperating domain are interleaved with the readout frequencies for thesame operating domain.

For example, FIGS. 21A-C show an example of interleaved qubit operatingfrequencies and readout frequencies, where the qubit operatingfrequencies and readout frequencies alternate along the frequencyspectrum plot. In some example interleaved schemes, each qubit deviceand its corresponding readout device operate within a frequency band,and the frequency band for each qubit and readout device pair isseparate and distinct (non-overlapping) with the frequency band for theother qubit and readout device pairs within the same operating domain.Each operating domain in a quantum computing system can have the sameallocation of frequency bands for the qubit and readout device pairs, orthe various operating domains can have distinct frequency bandallocations.

In some implementations, the qubit operating frequencies for anoperating domain are not interleaved with the readout frequencies forthe same operating domain. For example, the qubit devices within anoperating domain can have respective qubit operating frequencies in afirst frequency band, and the readout devices in the operating domaincan have respective readout frequencies in a second, separate frequencyband. In such cases, the qubit operating frequencies fall within onesub-band of the frequency spectrum, and the readout frequencies fallwithin a different sub-band of the frequency spectrum. In some examplenon-interleaved schemes, the qubit frequency band (the frequency bandthat contains the qubit operating frequencies) for a group of qubitdevices within an operating domain is separate and distinct(non-overlapping) from the readout frequency band (the frequency bandthat contains the readout frequencies) for the group of readout devicesin the same operating domain. The readout frequency band can be higheror lower than the qubit frequency band. Each operating domain can havethe same allocation of operating frequencies, qubit frequency bands andreadout frequency bands, or the various operating domains can havedistinct frequency bands and operating frequency allocations.

The example quantum computing system 2300 illustrates four distinctoperating domains, and each operating domain includes four of the qubitdevices. Thus, there are sixteen qubit devices, sixteen readout devices,and twenty-four coupler devices that are controlled by four operatingdomains in the quantum computing system 2300. A quantum computing system2300 can include another number of operating domains, and each domainmay generally include another number of devices.

In the example shown in FIG. 23A, the control system components thatoperate in the room temperature stage 2301 include a signal generatorsystem 2302, a signal processor system 2310, and a control interface2305. Additional or different components may operate in the roomtemperature stage 2301. The example signal generator system 2302includes a microwave signal generator 2304, and may include additionalor different components.

In some cases, the signal generator system 2302 also includes a DCcontrol system. For example, the DC control system can provide DCcontrol signals to the coupler devices. In some cases, the signalgenerator system 2302 includes a dedicated DC control system for eachoperating domain. In the example shown in FIG. 23A, the signal generatorsystem 2302 can include four DC control systems, where each DC controlsystem controls six of the twenty-four coupler devices. For instance,each of the DC control systems can be a six-channel DC control systemthat is capable of providing a distinct DC control signal to eachcoupler device in the operating domain.

In some instances, the signal generator system 2302 includes a microwavesignal generator 2304 for each of the operating domains. The microwavesignal generator system 2304 can include an arbitrary waveform generator(AWG) that generates multiplexed control signals for an operating domainon a single physical channel. For example, the signal generator system2302 may have an output channel for each operating domain, and thecontrol signals generated on each output channel can include multiplexedcontrol signals for multiple devices in the operating domain. In theexample shown in FIG. 23A, signals from the microwave signal generator2304 are communicated on four distinct channels, as indicated at 2306.

The microwave signal generator 2304 can generate analog control signalsbased on digital control information received from the control interface2305. For example, the control interface 2305 may provide a digitalmultiplexed control signal for a group of devices in the quantumprocessor cell, and the microwave signal generator can generate ananalog multiplexed control signal that corresponds to the digitalmultiplexed control signal. Each analog multiplexed control signal canbe communicated into the cryogenic environment on a single physicalchannel in some instances.

The example signal processor system 2310 includes a digitizer 2312, amixer and a microwave source 2314 for each operating domain. The signalprocessor system 2310 can receive qubit readout signals and convert thequbit readout signals to qubit readout information that can be used todetermine the quantum states of the qubit devices. For example, thequbit readout signals can be analog qubit readout signals from thesignal delivery system, and the signal processor system 2310 can convertthe analog qubit readout signals to digital qubit readout information.The qubit readout information can be delivered to the control interface2305 where the information can be processed, for example, by a classicalprocessor running software or dedicated classical processing hardware.

In some cases, the qubit readout signals received by the signalprocessor system 2310 are multiplexed signals that include readoutsignals from multiple readout devices. For instance, each multiplexedreadout signal can include readout signals from multiple devices in anoperating domain. The control interface 2305 can digitally de-multiplexthe readout signals after they have been digitized by the signalprocessor system 2310, or the signal processor system 2310 may extractqubit readout information directly from the digitized readout outputpulses and send digital data to the control interface 2305, forinstance.

The example quantum computing system 2300 includes a multichannel signalamplifier 2320 and a multichannel isolator 2322 in the intermediatetemperature stages 2321. The quantum computing system 2300 may includeadditional or different features and components operating in one or moreintermediate temperature stages. In the example shown, the multichannelsignal amplifier 2320 can amplify or otherwise modulate signals that arecommunicated between the room temperature environment and the cryogenicenvironment. The multichannel isolator 2322 can isolate the signal linesbetween the cryogenic environment and the multichannel signal amplifier2320. In the example shown, the multichannel isolator 2322 can be afour-channel isolator that isolates a signal line for each operatingdomain.

In the cryogenic temperature stage 2331, the example quantum computingsystem 2300 includes an input board 2330, an input interconnect system2342, a quantum processor cell (QPC) assembly 2346, an outputinterconnect system 2344 and an output board 2350. The example quantumcomputing system 2300 can include additional or different features andcomponents in the cryogenic temperature stage, and the components can bearranged or configured in the manner shown or in another manner.

The components operating in the cryogenic temperature stage 2331 receiveinput signals through the input board 2330, and send out signals throughthe output board 2350. Input control signals can be communicated to theinput board 2330 on a distinct channel for each operating domain. In theexample shown in FIG. 23A, four distinct input channels are indicated at2335, where each of the channels receives AC control signals for one ofthe operating domains. Similarly, output control signals can becommunicated from the output board 2350 on a distinct channel for eachoperating domain. In the example shown in FIG. 23A, four distinct outputchannels are shown, where each of the channels carries AC readoutsignals for one of the operating domains. In some examples, the inputboard 2330 includes additional input channels to receive DC controlsignals (e.g., from the signal generator system 2302). For example, theinput board 2330 may receive one or more DC control signals for eachcoupler device.

In some cases, the example input board 2330 can be implemented as one ormore structures that support signal processing components. For example,the input board 2330 can be or can include the example input processingboard 270A shown in FIG. 20D or another system. In some implementations,the input board 2330 can be or can include a multilayered microwaveprinted circuit board, or another type of circuit board structure. Theexample input board 2330 includes output channels that contact inputchannels of the input interconnect system 2342. Thus, the input board2330 can communicate control signals into the QPC assembly 2346 throughthe input interconnect system 2342. The input interconnect system 2342can be or can include the example input interconnect plate 135 shown inFIG. 20B or another system.

The example input board 2330 can be formed as a multilayered structurethat includes multiple layers of insulative material, for instance, withconducting or superconducting materials between some of the layers toform transmission lines. For instance, the insulative material caninclude multiple layers of silicon, sapphire, diamond, or othermaterials that form a multilayer structure by wafer bonding. In someimplementations, the insulative material can include Rogers 3000-serieslaminate (available from Rogers Corporation), which may have, forexample, a low coefficient of thermal expansion in the “z” direction anddielectric constants ranging from 3 to 10.2. In some examples, Rogers3010 (dielectric constant=10.2), Rogers 6010 (dielectric constant=10.2),Rogers 4350 (dielectric constant=3.48), or another laminate material canbe used. In some cases, a laminate material can include a transitionbetween dielectric constants. In some cases, a laminate material iscapable of high layer count constructions. A laminate material caninclude, for example, ceramic-filled PTFE composites or other materials.

The example input board 2330 includes an input processing subsystem2332. The example input processing subsystem 2332 can include multipleinput processing domains; for example, a dedicated input processingdomain can process input signals for each operating domain of thequantum computing system 2300. In the example shown, the inputprocessing subsystem 2332 includes four input processing domains, andeach input processing domain receives and processes control signals forthe devices (qubit devices, coupler devices, readout devices) within oneof the operating domains.

Each input processing domain can be similar or identical to the otherinput processing domains. For example, the hardware for each inputprocessing domain can be the same as the hardware for one or more of theother input processing domains. In some implementations, each inputprocessing domain can include multiple processing cards that aresupported on the input board 2330. The processing cards for one inputprocessing domain may be interchangeable with one or more of theprocessing cards in another input processing domain.

In some implementations, processing cards are supported in receptacleslots defined in the input board 2330. The processing cards included inthe example input board 2330 can be implemented as discrete devices thatare mechanically secured and communicably coupled to the input board2330. Each of the processing cards can include signal processinghardware configured to process (e.g., diplex, multiplex, de-multiplex,filter, bias, etc.) control signals, and the input board 2330 caninclude signal lines that transfer signals between the distinctprocessing cards. The processing cards can include transmission linesthat carry signals within the processing card. For example, thetransmission lines may include coplanar waveguide (CPW) structures. Insome instances, coplanar waveguide (CPW) structures can be implementedas layered structures, with superconducting planes on the top and bottomof an insulating material, and a signal-carrying trace in the middle ofthe insulative material. In some instances, dielectric or insulativematerial in the processing cards can include silicon, sapphire, fusedquartz, diamond, beryllium oxide (BeO), aluminum nitride (AlN), orothers.

In the example shown, each input processing domain of the inputprocessing subsystem 2332 includes a diplexer 2334, a de-multiplexer2336, a DC bias component 2338 and a de-multiplexer 2340. Each of thecomponents may be implemented, for example, in one or more processingcards on the input board 2330. The input processing subsystem 2332 mayinclude additional or different components, and the components may beconfigured as shown or in another manner.

The example diplexer 2334 can separate input signals onto two distinctoutput channels based on the frequencies of the input signals. Forexample, the diplexer 2334 can separate low-frequency control signalsfrom high-frequency control signals. In some examples, the drive signalsfor the coupler devices are all within a lower frequency band than thecontrol signals for the qubit and readout devices. For example, in theexample shown in FIGS. 22A-C, the qubit operating frequencies are in therange of 3.2 to 3.9 GHz, and the drive frequencies for the couplerdevices are in the range of 0.1 GHz to 0.7 GHz. Thus, the diplexer 2334can receive input signals ranging from a few MHz to high microwavefrequencies, and send lower frequency signals to a first device and sendhigher frequency signals to a second device. In an exampleimplementation, the diplexer 2334 sends low-frequency signals (e.g., 225MHz through 1.375 GHz, or another frequency range) to the firstde-multiplexer 2336, and the diplexer 2334 sends high-frequency signals(e.g., above 2.5 GHz, or another threshold frequency) to the secondde-multiplexer 2340.

Each of the de-multiplexers 2336, 2340 separates input signals ontomultiple distinct output channels based on the frequencies of the inputsignals. For example, each de-multiplexer can receive an input signalthat includes multiple frequency components, and separate the distinctfrequency components onto distinct output channels.

The example de-multiplexer 2340 receives the qubit control signals andthe readout control signals, which are microwave-frequency signalsaddressed to the respective qubit devices and readout devices. The qubitcontrol signals and the readout control signals for a group of qubitdevices and readout devices are delivered on a single input channel tothe de-multiplexer 2340, and the de-multiplexer separates the controlsignal for each individual qubit device onto the distinct physicaloutput channels. In the example shown, the de-multiplexer 2340 is a 1:4de-multiplexer that receives the high-frequency band output from thediplexer 2334 (e.g., 3 GHz to 4 GHz, or another frequency range).

The example de-multiplexer 2336 receives the AC components of thecoupler control signals, which are radio-frequency ormicrowave-frequency drive signals addressed to the respective couplerdevices. In some instances, the drive signals for a group couplerdevices are delivered on a single input channel to the de-multiplexer2336, and the de-multiplexer 2336 separates the drive signal for eachindividual coupler device onto a distinct physical output channel. Inthe example shown, the de-multiplexer 2336 is a 1:6 de-multiplexer thatreceives the low-frequency band output from the diplexer 2334 (e.g., 225MHz through 1.375 GHz, or another frequency range).

The example DC bias component 2338 receives the drive signals from thede-multiplexer 2336 and adds a bias signal to each drive signal. Thebias can be a low frequency or DC component of the coupler controlsignal. For example, the bias signal can be configured to tune thecoupler device to a particular coupler operating frequency or biaspoint. In some cases, the DC component causes the coupler device toproduce and offset electrical or magnetic field that tunes the couplerdevice and produces a higher rate of coupling between neighboring qubitdevices. The bias signal in each coupler control signal can beconfigured for a particular control device. Thus, the DC bias component2338 can apply distinct bias levels to distinct drive signals receivedfrom the de-multiplexer 2336. In some cases, the bias signals arereceived through a separate input of the input board 2330.

The input board 2330 can include an output channel for each qubit deviceand each coupler device in the QPC assembly 2346. In the particularexample shown in FIG. 23A, there are forty output channels from theinput board 2330, which includes ten output channels for each operatingdomain. Within each operating domain, there are six coupler controlsignal output channels from the input board 2330, and there are fourqubit control signal output channels from the input board 2330. Thus, inthe example shown, there are twenty-four output channels from the DCbias components 2338 to the input interconnect system 2342, and thereare sixteen output channels from the second de-multiplexer 2340 to theinput interconnect system 2342.

The example configuration shown in FIG. 23A can be used with aninterleaved frequency scheme, where the qubit operating frequencies areinterleaved with the readout frequencies. In some cases, theconfiguration shown in FIG. 23A can be used or adapted for use with anon-interleaved frequency scheme, for example, where the qubit operatingfrequencies are in a distinct band from the readout frequencies. For anexample non-interleaved scheme, the input processing subsystem 2332 mayinclude an additional diplexer and an additional de-multiplexer for eachoperating domain. The additional diplexer can operate between thediplexer 2334 and the second de-multiplexer 2340, and can separate qubitcontrol signals (in a qubit frequency band) from readout control signals(in a readout frequency band). The qubit control signals can bedelivered to the second de-multiplexer 2340, and the readout controlsignals can be delivered to the additional (third) de-multiplexer. Thethird de-multiplexer can be a 1:4 de-multiplexer that separates fourreadout control signals from a multiplexed control signal. In suchexamples, the input board 2330 includes sixteen additional outputchannels from the third de-multiplexer to the input interconnect system2342.

The example QPC assembly 2346 houses the qubit devices, the couplerdevices and the readout devices of the quantum computing system 2300.The qubit devices, the coupler devices and the readout devices may behoused, for example, in an electromagnetic waveguide system or anotherstructure. The QPC assembly 2346 can be constructed according to theexample quantum processor cells shown and described with respect toFIGS. 1-22, or the QPC assembly 2346 can be constructed and may operatein another manner. The example QPC assembly 2346 includes atwo-dimensional array of sixteen qubit devices, with twenty-four couplerdevices residing at intervals between the sixteen qubit devices in thearray, and with sixteen readout devices each associated with anindividual qubit device. The quantum computing system 2300 can beadapted to include other types of multi-dimensional qubit arrays andarrays of other sizes. For example, the quantum computing system 2300may include a two- or three-dimensional array of tens or hundreds ofqubit devices and appropriate coupler devices and readout devicesassociated therewith. These arrays may be tiled and repeated adjacent toone another or in an interpenetrated manner to construct arrays ofarbitrary size for large-scale quantum computing.

The example output board 2350 can be implemented as one or morestructures that support signal processing components. For example, theoutput board 2350 can be or can include the example output processingboard 270B shown in FIG. 20E or another type of system. In someimplementations, the output board 2350 can be a multilayered microwaveprinted circuit board, or another type of circuit board structure. Theexample output board 2350 includes input channels that contact outputchannels of the output interconnect system 2344. Thus, the output board2350 can receive qubit readout signals from the QPC assembly 2346through the output interconnect system 2344. The output interconnectsystem 2344 can be or can include the example output interconnect plate139 shown in FIG. 20C. In some examples, the output board 2350 includesadditional input channels, for example, to receive pump signals forparametric amplifiers, etc.

In some implementations, the output board 2350 can be formed as amultilayered structure that includes multiple layers of insulativematerial, for instance, with conducting or superconducting materialsbetween some of the layers to form transmission lines. For instance, theinsulative material can include the materials described above withrespect to the input board 2330 (e.g., silicon, sapphire, diamond,laminate materials available from Rogers Corporation, etc.).

The example output board 2350 includes an output processing subsystem2352. The example output processing subsystem 2352 can include multipleoutput processing domains; for example, a dedicated output processingdomain can process output signals for each operating domain of thequantum computing system 2300. In the example shown, the outputprocessing subsystem 2352 includes four output processing domains, andeach output processing domain receives qubit readout signals from thereadout devices within one of the operating domains.

Each output processing domain can be similar or identical to the otheroutput processing domains. For example, the hardware for each outputprocessing domain can be the same as the hardware for one or more of theother output processing domains.

For instance, each output processing domain can include multipleprocessing cards that are supported on the output board 2350. Theprocessing cards for one output processing domain may be interchangeablewith one or more of the processing cards in another output processingdomain.

In some implementations, processing cards are supported in receptacleslots defined in the output board 2350. The processing cards included inthe example output board 2350 can be implemented using hardware andtechniques that are similar to the processing cards in the example inputboard 2330. For example, the processing cards can be mechanicallysecured and communicably coupled to the output board 2350. Each of theprocessing cards can include signal processing hardware configured toprocess (e.g., filter, multiplex, amplify, de-multiplex, isolate, etc.)readout signals. The processing cards can include transmission lines(e.g., coplanar waveguide (CPW) structures or others) that carry signalswithin the processing card, and the output board 2350 can include signallines the transfer signals between the distinct processing cards.

In the example shown, each output processing domain of the outputprocessing subsystem 2352 includes a multichannel isolator 2354, andamplifier 2356 and a multiplexer 2358. The components may beimplemented, for example, by one or more processing cards. The outputprocessing subsystem 2352 may include additional or differentcomponents, and the components may be configured as shown or in anothermanner.

The example multichannel isolator 2354 can isolate the input channelsbetween the output interconnect system 2344 and the amplifier 2356. Inthe example shown, the multichannel isolator 2354 and each operatingdomain can be a four-channel isolator that isolates a signal line foreach qubit device in the operating domain. The isolator can includemagnetic or electromagnetic shielding in some instances.

The example amplifier 2356 can amplify the qubit readout signalsreceived from the multichannel isolator 2354. For example, the amplifier2356 can receive power from an external power source and increase thevoltage of the qubit readout signals. In some examples, the outputprocessing subsystem includes a power divider for each operating domain,and the power divider receives power from the external system anddelivers appropriate power levels to input ports of the amplifier 2356.

The example multiplexer 2358 receives the qubit readout signals, whichare microwave-frequency signals from the respective readout devices.Each of the qubit readout signals is delivered to the multiplexer 2358on a distinct input channel, and the multiplexer combines the qubitreadout signals onto a single physical output channel. The qubit readoutsignals within an operating domain are in distinct frequency ranges, andthe multiplexed signal produced by the multiplexer 2358 includesmultiple frequency components corresponding to the multiple readoutfrequencies. In the example shown, the multiplexer 2358 is a 4:1multiplexer that receives qubit readout signals in an operatingfrequency band (e.g., 3 GHz to 4 GHz, or another frequency range). Forinstance, the multiplexer 2358 can be similar or identical to thede-multiplexer 2340, but with the input and output ports interchanged.

The output board 2350 can include an input channel for each qubit devicein the QPC assembly 2346. In the particular example shown in FIG. 23A,there are sixteen input channels from the output interconnect system2344, which includes four input channels for each operating domain. Theoutput board 2350 can include an output channel for each group of qubitdevices in the QPC assembly 2346 (where each group of qubit devicescorresponds to an individual operating domain of the quantum computingsystem 2300). In the particular example shown in FIG. 23A, there arefour output channels from the output board 2350, which includes oneoutput channel for each operating domain.

In some instances, the quantum computing system 2300 can perform quantumcomputational tasks, execute quantum computing algorithms, performquantum error correction, quantum state distillation, or perform othertypes of processes. For instance, the control interface 2305 can includea quantum compiler and a master clock, and can operate the quantumcomputing system on clock cycles, where a set of instructions areexecuted by the quantum computing system 2300 on each clock cycle. Forexample, the control interface 2305 can generate control information foreach clock cycle according to a set of instructions from a quantumcompiler; the signal generator system 2302 can receive the controlinformation from the control interface 2305 and generate control signalsthat are delivered to the input board 2330. The control interface 2305may also receive qubit readout data on each clock cycle. For example,the signal processor system 2310 can receive readout signals from theoutput board 2350 and generate digital readout data that is delivered tothe control interface 2305. In some implementations, the quantumcomputing system 2300 can operate in another manner.

In some instances, the control interface 2305 generates quantumprocessor control information that includes digital control informationfor multiple devices in the QPC assembly 2346. For example, the controlinterface 2305 may generate a digital control sequence for a group ofqubit devices, a group of readout devices, a group of coupler devices, agroup of amplifier devices, a group of other devices, or a combinationof them. In some instances, the digital control information correspondsto pulses or other types of control signals to be delivered toindividual devices. The control interface 2305 can digitally multiplexthe digital control information for groups of devices in the QPCassembly 2346. For example, the control interface may digitallymultiplex the digital control information for the group of qubit deviceswithin each operating domain of the quantum computing system 2300. Theoperations performed by the control interface 2305 can be implemented,for example, by one or more data processors or other types of classicalcomputing equipment.

In some instances, the digital control information generated by thecontrol interface 2305 includes qubit control information for a group ofqubit devices that operate in a common operating domain and each havedistinct qubit operating frequencies. For instance, the qubit controlinformation can include qubit control sequences for respective qubitdevices in the group, and the qubit control sequence for each qubitdevice can be configured to execute a single-qubit operation on thequbit device.

In some instances, the digital control information generated by thecontrol interface 2305 includes coupler control information for a groupof coupler devices that operate in a common operating domain and eachhave distinct operating frequencies.

For instance, the coupler control information can include couplercontrol sequences for each respective coupler device in the group, andthe coupler control sequence for each coupler device can be configuredto execute a two-qubit operation on a pair of qubit devices thatneighbor the coupler device.

In some instances, the digital control information generated by thecontrol interface 2305 includes readout control information for a groupof readout devices that operate in a common operating domain and eachhave distinct readout frequencies. For instance, the readout controlinformation can include readout control sequences for each respectivereadout device in the group, and the readout control sequence for eachreadout device can be configured to execute a readout operation on aqubit device associated with the readout device.

In some instances, the digital control information generated by thecontrol interface 2305 includes a combination of qubit controlinformation and coupler control information or another combination ofcontrol sequences that are configured to perform all or part of aquantum algorithm, a quantum error correction protocol, a statedistillation protocol, one or more quantum logic gates, a quantummeasurement, or other types of quantum computational tasks. In someinstances, the digital control information generated by the controlinterface 2305 includes a combination of readout control information andother control information (e.g., qubit or coupler or both).

In some instances, the signal generator system 2302 receives the quantumprocessor control information from the control interface 2305 andgenerates a multiplexed control signal based on the quantum processorcontrol information. For example, the quantum processor controlinformation can include the digitally multiplexed control informationfor a group of devices (e.g., qubit devices, readout devices, couplerdevices, or a combination), and the signal generator system 2302 cangenerate an analog control signal that is communicated from the signalgenerator system 2302 on a single physical channel. The signal generatorsystem 2302 can communicate multiplexed control signals on each of thefour output channels indicated at 2306, and each of the output channelscarries multiplexed control signals for an individual operating domain.

Because, in the example quantum computing system 2300, the signalgenerator system 2302 operates in the room temperature stage 2301, themultiplexed control signals are generated in a room temperatureenvironment. The multiplexed control signals are communicated into thecryogenic temperature stage 2331 through the intermediate temperaturestage 2321. In some cases, the multiplexed control signals are microwavecontrol signals that are communicated by a microwave waveguide oranother type of transmission line. In the example shown, the multiplexedcontrol signals are amplified by the multichannel signal amplifier 2320in the intermediate temperature stage 2321 before they are communicatedinto the cryogenic temperature stage 2331.

In some instances, the signal generator system 2302 or signal processorsystem 2310 or control interface 2305 may be operated on hardware in acryogenic environment. In some instances, the cryogenic environment maybe at a temperature below room temperature but above the temperature ofthe QPC operating environment.

In some instances, each input processing domain of the input processingsubsystem 2332 on the input board 2330 receives a multiplexed controlsignal for a group of devices in the QPC assembly 2346. For instance,each input processing domain can include an input channel configured toreceive the respective multiplexed control signal. The de-multiplexerdevices in each input processing domain of the input processingsubsystem 2332 can separate device control signals from the multiplexedcontrol signal by de-multiplexing the multiplexed control signal. Forexample, the de-multiplexer 2336 can separate six distinct drive signalsfrom a multiplexed control signal, and the de-multiplexer 2340 canseparate four distinct control signals from a multiplexed controlsignal. Because the input processing subsystem 2332 operates in thecryogenic temperature stage 2331, the multiplexed control signals arede-multiplexed in a low-noise, cryogenic environment.

The device control signals for each respective device are delivered intothe QPC assembly 2346 on respective channels through the inputinterconnect system 2342. For instance, the input signal processingsubsystem 2332 can include output channels configured to communicate therespective device control signals into the QPC assembly 2346 through theinput interconnect system 2342. In some instances, the inputinterconnect system 2342 includes input interconnect signal lines thatextend from an exterior of the QPC assembly 2346 to the interior of theQPC assembly 2346.

The input interconnect signal lines can include a first end thatcontacts an output channel of the input board 2330, and a second endthat contacts a lead that is inside the QPC assembly 2346 (e.g., on aplateau of the signal board). The input interconnect signal lines can besupported within the QPC assembly 2346, for example, by plateaustructures that extend vertically with respect to the plane of thetwo-dimensional device array in the QPC assembly 2346.

The QPC assembly 2346 may include a signal board or another type ofstructure that supports the qubit devices, coupler devices, and readoutdevices within the QPC assembly 2346. For example, the QPC assembly 2346may include the example signal board 140A shown in FIGS. 10A-10B and11A-11B, or another type of signal board. The signal board can includeinput signal lines that route the device control signals within thequantum processor cell to the respective devices. For example, eachinput signal line in the signal board can have a first end that contactsa lead on the input interconnect system 2342 and a second end thatcouples (e.g., conductively, capacitively, inductively, etc.) to adevice supported by the signal board. In some instances the signal boardcan deliver signals from the exterior volume of an electromagneticwaveguide system to an enclosed or partially enclosed interior volume ofan electromagnetic waveguide system.

In some instances, the readout devices in the QPC assembly 2346 producequbit readout signals based on readout control signals received from thecontrol system. For instance, the qubit readout signals can be producedby the respective readout device based on an electromagnetic interactionbetween the readout device and the associated qubit device in responseto the readout control signal. In some cases, each readout device isoperatively coupled (e.g., capacitively, conductively, inductively, orotherwise coupled) to an individual qubit device. In some cases, thereadout device is coupled to the qubit device through an aperture in theelectromagnetic waveguide system. The readout device can, in some cases,be located in a partially interior and partially exterior volume of thewaveguide system.

In some instances, the qubit readout signals produced by each respectivereadout device are communicated from the readout devices by signal linesincluded in the signal board that supports the devices within the QPCassembly 2346. For example, the signal board can include output signallines that route the qubit readout signals within the QPC assembly 2346to the output interconnect system 2344. Each output signal line in thesignal board can have a first end that couples (e.g., conductively,inductively, capacitively, etc.) to a readout device supported by thesignal board, and a second end that contacts a lead on the outputinterconnect system 2344. Readout signal lines can in some instancesinclude planar or three-dimensional filter structures used to modify theimpedance of the signal line at the operating frequencies of theassociated readout device, qubit device or coupler devices connected tothe associated qubit device.

In some instances, the qubit readout signals for each respective readoutdevice are delivered to the output board 2350 on respective channelsthrough the output interconnect system 2344. The example outputinterconnect system 2344 includes output interconnect signal lines thatextend from an interior of the QPC assembly 2346 to an exterior of theQPC assembly 2346. The output interconnect signal lines can each includea first end that contacts a lead inside the QPC assembly 2346 (e.g., ona plateau of the signal board), and a second end that contacts and inputchannel of the output board 2350. The output interconnect signal linescan be supported within the QPC assembly 2346, for example, by plateaustructures that extend vertically with respect to the plane of thetwo-dimensional device array in the QPC assembly 2346. The output signalprocessing system 2352 can include input channels configured to receivethe respective qubit readout control signals from the outputinterconnect system 2344.

Each output processing domain in the output signal processing system2352 on the output board 2350 receives qubit readout signals from arespective group of the readout devices (which correspond to arespective operating domain of the quantum computing system 2300). Insome instances, each readout device in the group has a distinct readoutfrequency. The multiplexer 2358 in each output processing domain canreceive the qubit readout signals from an individual group of thereadout devices and generate a multiplexed readout signal bymultiplexing the qubit readout signals. For example, the multiplexer2358 can receive four distinct qubit readout signals and generate asingle multiplexed readout signal. Because the multiplexer 2358 operatesin the cryogenic temperature stage 2331, the qubit readout signals aremultiplexed in a low-noise, cryogenic environment.

In some instances, the multiplexed readout signals are communicated fromthe output board 2350 on a respective physical channel for eachoperating domain. For instance, a multiplexed readout signal thatcontains qubit readout signals from four readout devices can becommunicated from the output board 2350 on a single channel.

The multiplexed readout signals are communicated from the cryogenictemperature stage 2331 through the intermediate temperature stage 2321.In some cases, the multiplexed readout signals are microwave signalsthat are communicated by a microwave waveguide or another type oftransmission line. In the example shown, the multiplexed readout signalsare amplified by the multichannel signal amplifier 2320 in theintermediate temperature stage 2321 before they are communicated intothe room temperature stage 2301. Other arrangements of the signal pathfor readout signals are possible.

In some instances, the signal processor system 2310 receives themultiplexed readout signals, performs analog filtering and processingand digitizes each multiplexed readout signal by operation of thedigitizer 2312, and performs digital signal processing of the digitizedsignal. For example, the qubit readout signals received by the outputboard 2350 and the multiplexed readout signals produced by the outputboard 2350 can be analog signals, and the signal processor system 2310can convert the multiplexed readout signals to digital information. Thesignal processor system 2310 can provide the digital readout informationto the control interface 2305, and the control system can process thedigital readout information. For example, digital readout informationfor an operating domain can be generated from the multiplexed readoutsignal for the operating domain, and the control interface 2305 canreceive the digital readout information for all operating domains.

In some instances, the control system identifies qubit readout data foreach readout device based on the digital readout information. Forexample, the control system can digitally de-multiplex the digitalreadout information from the signal processor system 2310 based on thedistinct operating frequencies of the respective readout devices in eachgroup. In some cases, the readout data for a readout device includes adigital data sequence representing the qubit readout signal produced bythe readout device. Thus, each qubit readout signal received by theoutput board 2350 can be converted to digital readout data by thecontrol system, for example, by de-multiplexing the digitized version ofthe multiplexed readout signal generated by the output board 2350.

In some instances, the control system prepares multiplexed quantumprocessor control information for the QPC assembly 2346 based on thequbit readout data. For instance, the multiplexed quantum processorcontrol information can be a digital control sequence for the next clockcycle of the quantum computing system 2300. In some cases, themultiplexed quantum processor control information is based on additionalor different information. For example, the multiplexed quantum processorcontrol information may be based on a quantum computing task or quantumalgorithm, or other information. In some cases, the multiplexed quantumprocessor control information is communicated from the control interface2305 to the signal generator system 2302, where it is processed anddelivered to the QPC assembly 2346 as described above. For instance, themultiplexed quantum processor control information may include qubitcontrol information for a group of qubit devices, coupler controlinformation for a group of coupler devices, readout control informationfor a group of readout devices, or a combination of them.

FIG. 23B is a flowchart showing an example process 2360 for operating aquantum computing system. For instance, the example process 2360 can beused to control an individual operating domain of the example quantumcomputing system 2300 shown in FIG. 23A. Some aspects of the exampleprocess 2360 may be implemented by one or more of the example componentsshown in FIG. 23A or by additional or different components. In somecases, the example process 2360 can be used to operate a device arraythat includes a frequency tiling or multiple frequency sub-arrays, suchas, for example, the device array 2120 shown in FIG. 21C, the devicearray 2220 shown in FIG. 22C, or another device array. The process 2360may include additional or different operations, and the operations canbe performed in the order shown in FIG. 23B or in another manner.

FIG. 23B shows a read/write channel controller 2361 that includes afield-programmable gate array (FPGA) 2362, an analog-to-digitalconverter (ADC) 2363 and a digital-to-analog converter (DAC) 2364. Insome implementations, the channel controller 2361 can be a widebandfrequency-agile signal generator such as an arbitrary waveformgenerator. The FPGA 2362 can control the DAC 2364 to produce a pulse orother signal having one or more frequency components targeted to one ormore qubit devices or readout devices. For example, the signal can beaddressed to an individual qubit device by generating the signal at afrequency that corresponds to the qubit operating frequency of the qubitdevice. As another example, the signal can be addressed to an individualreadout device by generating a signal at a frequency that corresponds tothe readout frequency of the readout device.

The signals generated by the channel controller 2361 can be multiplexedin time or in frequency, and they may be separated onto physicallydisparate signal paths. For example, the signals may be separated ontodistinct channels through power division followed by passive frequencyselective filtering, or by the use of a fast solid state microwaveswitch, switched in synchronicity with the time-multiplexing of thesignal, to dynamically separate the outgoing signals.

As shown in FIG. 23B, the example process 2360 includes an exampletechnique for processing the signals between the channel controller 2361and the quantum processor cell 2371. At 2365, signals from the channelcontroller 2361 are filtered. At 2366, the filtered signals areprocessed by dissipative attenuation. At 2367, the signals are processedby a cryogenic low-noise amplifier. At 2368, the amplified signals passthrough a directional coupler. At 2369, the signals are divided by adiplexer. The diplexer separates write signals from read signals, forexample, based on a multiplexing scheme (e.g., time multiplexing orfrequency multiplexing).

In the example shown in FIG. 23B, the write signals from the diplexerare processed by a frequency multiplexer at 2370. The frequencymultiplexer divides a multiplexed write signal onto multiple outputchannels. For example, the write signals can be delivered to the writeports of the quantum processor cell 2371 through a frequency channelizedwrite signal array.

In the example shown in FIG. 23B, the read signals from the diplexer areprocessed by a frequency multiplexer at 2372. The frequency multiplexerdivides a multiplexed read signal onto multiple output channels. Forexample, the read signals can be delivered to an m-channel circulatorbank through a frequency channelized read signal array. At 2373, theread signals are circulated through a circulator bank to read ports ofthe quantum processor cell 2371. In some cases, signal circulation canbe performed, for example, by a many-channel shielded ferrite corecirculator or isolator bank on printed circuit board substrates forlow-loss high-density circulation of RF signals. Other types ofcirculators may be used.

Readout devices in the quantum processor cell 2371 can produce qubitreadout signals in response to the read signals. As shown in FIG. 23B,the example process 2360 includes an example technique for processingthe readout signals between the quantum processor cell 2371 and thechannel controller 2361. The qubit readout signals are communicated fromthe read ports to the m-channel circulator bank. At 2373, the qubitreadout signals are circulated through the circulator bank to acryogenic low noise amplifier bank. At 2374, the qubit readout signalsare amplified by the cryogenic low noise amplifier bank. At 2375, theamplified qubit readout signals are multiplexed to produce a multiplexedreadout signal. At 2376, the multiplexed readout signal isdown-converted. At 2377, the down-converted signal is filtered anddelivered to the channel controller 2361. The ADC 2363 can digitize themultiplexed readout signals and deliver them to the FPGA 2362.

FIG. 24 is a flowchart showing an example process 2400 for deliveringcontrol signals to a quantum processor cell. For instance, the exampleprocess 2400 can be used to deliver control signals for an individualoperating domain of the example quantum computing system 2300 shown inFIG. 23A. Some aspects of the example process 2400 may be implemented byone or more of the example components shown in FIG. 23A or by additionalor different components. In some cases, the example process 2400 can beused to operate a device array that includes a frequency tiling ormultiple frequency sub-arrays, such as, for example, the device array2120 shown in FIG. 21C, the device array 2220 shown in FIG. 22C, oranother device array. In some implementations of the process 2400 shownin FIG. 24, multiplexed composite pulses are composed and synthesized ata higher temperature (e.g., in a room temperature stage or anintermediate temperature stage), and the pulses are de-multiplexed anddelivered at a lower temperature (e.g., in a cryogenic temperaturestage). The process 2400 may include additional or different operations,and the operations can be performed in the order shown in FIG. 24 or inanother manner.

At 2410, control information is generated for individual devices in aquantum processor cell. For example, the control information can includea control sequence for each individual device (a qubit device, couplerdevice, a readout device). Each control sequence can include digitalinformation and can be generated by a classical computing system runninga software program. For example, the digital information can begenerated by code running in Python or MATLAB® software (available fromThe MathWorks, Inc.) or another type of software program.

In the example shown in FIG. 24, the control information includes pulseinformation for each of n subsystems. Each subsystem can include, forexample, a qubit device, a coupler device, or readout device. Theexample pulse information 2411A represents a parameterized pulse forsubsystem 1, the example pulse information 2411B represents aparameterized pulse for subsystem 2, and the example pulse information2411C represents a parameterized pulse for subsystem n. Each pulse maybe parameterized, for example, based on an operation to be performed bythe subsystem. Moreover, the frequency of each pulse can be determinedaccording to an operating frequency of the subsystem to which the pulseis addressed. In the example shown, each subsystem has a distinctoperating frequency, and therefore, each pulse is centered on a distinctfrequency.

At 2420, a multiplexed, composite pulse is composed from the controlinformation. For example, the pulse information (2411A, 2411B, 2411C)for each subsystem can be combined to compose the multiplexed, compositepulse. The composite pulse composed at 2420 can include digitalinformation and can be generated by a classical computing system runninga software program. For example, the composite pulse can be generated byMATLAB® (available from The MathWorks, Inc.) or another type of softwareprogram. As such, the composite pulse can be generated by digitalmultiplexing or other techniques.

At 2430, the multiplexed, composite pulse is synthesized. The compositepulse synthesized at 2430 can be an analog signal generated by awaveform generator system. For example, the composite pulse can begenerated by an arbitrary waveform generator (AWG) based on the digitalversion of the composite pulse composed at 2420. Thus, the compositepulse synthesized at 2430 can be, for example, a radio frequency ormicrowave frequency pulse produced on a physical transmission line. At2440, the analog composite pulse generated at 2430 is delivered, forexample, on a single physical transmission line or a single series ofphysical transmission lines. In some cases, the analog composite pulseis delivered to an input processing system associated with a quantumprocessor cell.

At 2450, the analog composite pulse generated at 2430 is de-multiplexed(or channelized) into component pulses. In the example shown, anindividual analog composite pulse is separated into n analog pulses, anindividual pulse for each of the n subsystems. At 2460, the analogpulses are delivered to the respective subsystems. For example, thepulses may be control signals that are communicated in parallel to thedistinct subsystems (e.g., qubit devices, coupler devices, readoutdevices), for example, on distinct parallel transmission lines.

In the example shown in FIG. 24, a first control signal 2461A isdelivered to subsystem 1, a second control signal 2461B is delivered tosubsystem 2, and a third control signal 2461C is delivered to subsystemn. The first control signal 2461A is an analog control signal thatcorresponds to the control sequence included in the digital pulseinformation 2411A; the second control signal 2461B is an analog controlsignal that corresponds to the control sequence included in the digitalpulse information 2411B; and the third control signal 2461C is an analogcontrol signal that corresponds to the control sequence included in thedigital pulse information 2411C. Thus, the component pulses generated at2450 and delivered at 2460 correspond to the control informationgenerated at 2410.

FIG. 25 is a block diagram showing an example process 2500 fordelivering control signals to a quantum processor cell. For instance,the example process 2500 can be used to deliver control signals for anindividual operating domain of the example quantum computing system 2300shown in FIG. 23A. In some cases, the example process 2500 can be usedto operate a device array that includes a frequency tiling or multiplefrequency sub-arrays, such as, for example, the device array 2120 shownin FIG. 21C, the device array 2220 shown in FIG. 22C, or another devicearray. The example process 2500 can be used, for example, to synthesizeand deliver a frequency-multiplexed, time-superposed control sequencethat is channelized by a multiplexer for delivery to individual devices(qubit devices, readout devices, coupler devices, etc.) in a quantumprocessor cell.

The block diagram shown in FIG. 25 includes a quantum logic controller2510, a channel controller 2520, a wideband digital-to-analog (DAC)converter 2530, and a channelizer 2550. Some aspects of the exampleprocess 2500 may be implemented by the example components shown in FIG.25, by one or more of the example components shown in FIG. 23A, or byadditional or different components In some implementations of theprocess 2500 shown in FIG. 25, frequency multiplexing of write/readsignals is performed at a higher temperature (e.g., in a roomtemperature stage or an intermediate temperature stage), andde-multiplexing of the write/read signals is performed at a lowertemperature (e.g., in a cryogenic temperature stage). The process 2500may include additional or different operations, and the operations canbe performed in the order shown in FIG. 25 or in another manner.

The example quantum logic controller 2510 receives data from the channelcontroller 2520 and sends instructions to the channel controller 2520.For example, the quantum logic controller 2510 may receive readout dataindicating the states of one or more qubit devices; and the quantumlogic controller 2510 may send instructions corresponding to a quantumlogic operation to be performed by the quantum processor cell.

The example channel controller 2520 and the wideband DAC 2530 mayoperate, for example, similar to the FPGA 2362 and ADC 2363 shown inFIG. 23B, or they may operate in another manner. As shown in FIG. 25,the channel controller 2520 composes a digital composite controlsequence based on instructions received from the quantum logiccontroller 2510, and the wideband DAC 2530 generates an analog compositecontrol sequence based on the digital composite control sequencereceived from the channel controller 2520.

In the example shown, the wideband DAC 2530 generatesfrequency-multiplexed control signals 2540. The frequency-multiplexedcontrol signal 2540 include a frequency-multiplexed composite writesignal 2542 and a frequency-multiplexed composite read signal 2544. Thefrequency-multiplexed composite write signal 2542 contains pulses atmultiple distinct write pulse frequencies (A₁ to A_(n)) that correspondto the distinct qubit operating frequencies of multiple qubit devices.The frequency-multiplexed composite read signal 2544 contains pulses atmultiple distinct read pulse frequencies (B₁ to B_(n)) that correspondto the distinct readout frequencies of multiple readout devices.

In the example shown, the frequency-multiplexed control signal 2540 isde-multiplexed (or channelized) by the channelizer 2550. On one outputchannel, the channelizer 2550 generates a first series of de-multiplexedcontrol signals 2560A; and on another output channel, the channelizer2550 generates a second, distinct series of de-multiplexed controlsignals 2560B. The de-multiplexed control signals 2560A include ade-multiplexed write signal 2562A and a de-multiplexed read signal2564A. The de-multiplexed control signals 2560B include a de-multiplexedwrite signal 2562B and a de-multiplexed read signal 2564B.

In the example shown, the de-multiplexed write signal 2562A has a firstwrite pulse frequency A₁ that is addressed to a first qubit device,which has a first qubit operating frequency; and the de-multiplexedwrite signal 2562B has a second, distinct write pulse frequency A_(n)that is addressed to a second qubit device, which has a distinct, secondqubit operating frequency. The de-multiplexed read signal 2564A has afirst read pulse frequency B₁ that is addressed to a first readoutdevice, which has a first readout frequency; and the de-multiplexed readsignal 2564B has a second, distinct read pulse frequency B_(n) that isaddressed to a second readout device, which has a distinct, secondreadout frequency.

In the example process 2500 shown in FIG. 25, the channelizer 2550includes an input port that receives a summation of electronic signalsthat each have a unique frequency content. The channelizer 2550 rejectsfrequency content outside of the pass bands of its respective outputports. Each output port contains a specific passband and bandwidth thatis matched with the bandwidth of an individual qubit device, readoutdevice, or coupler device.

The example architecture shown in FIG. 25 may provide advantages, insome instances, for controlling the quantum processor cell. For example,the architecture may enable control signals to be delivered by asignificantly smaller number of electronic components and signalchannels. Reducing the number of electronic components can significantlyreduce the cost and complexity of the quantum computing system.Moreover, reducing the number of signal lines can significantly reducethe interface between cryogenic temperature stages and highertemperature stages, which may improve shielding and isolation of thequantum processor cell.

FIG. 26 is a block diagram showing an example process 2600 fordelivering qubit readout signals from a quantum processor cell. Forinstance, the example process 2600 can be used to deliver qubit readoutsignals for an individual operating domain of the example quantumcomputing system 2300 shown in FIG. 23A. In some cases, the exampleprocess 2600 can be used to operate a device array that includes afrequency tiling or multiple frequency sub-arrays, such as, for example,the device array 2120 shown in FIG. 21C, the device array 2220 shown inFIG. 22C, or another device array.

The block diagram shown in FIG. 26 includes a multiplexer 2620 and awideband ADC 2640. Some aspects of the example process 2600 may beimplemented by the example components shown in FIG. 26, by one or moreof the example components shown in FIG. 23A, or by additional ordifferent components. In some implementations of the process 2600 shownin FIG. 26, multiplexing of qubit readout signals is performed at alower temperature (e.g., in a cryogenic temperature stage), andde-multiplexing of the qubit readout signals is performed at a highertemperature (e.g., in a room temperature stage or an intermediatetemperature stage). The process 2600 may include additional or differentoperations, and the operations can be performed in the order shown inFIG. 26 or in another manner.

The example multiplexer 2620 shown in FIG. 26 receives qubit readoutsignals produced by n readout devices interacting with n qubit devicesin a quantum processor cell. Thus, each of the qubit readout signals isreceived from a distinct qubit device. The frequency distributions ofthree example qubit readout signals are plotted schematically in FIG.26. The horizontal axis in each of the three plots represents frequency,and the vertical axis in each of the three plots represents theamplitude of the qubit readout signal at each frequency. The first qubitreadout signal 2610A is centered on a first readout frequency f1, thesecond qubit readout signal 2610B is centered on a second readoutfrequency f2, and the third qubit readout signal 2610C is centered on athird readout frequency fn. The three readout frequencies (f1, f2, fn)are distinct because each qubit readout signal is generated (e.g., by acontrol system) for a readout device that operates at a distinct readoutfrequency.

The example multiplexer 2620 combines the n qubit readout signals togenerate a multiplexed readout signal 2630 for all n of the qubitdevices. Thus, the qubit readout signals from the n qubit devices can becommunicated on a single physical channel. The frequency distribution ofthe multiplexed readout signal 2630 is plotted schematically in FIG. 26.The horizontal axis in the plot represents frequency, and the verticalaxis of the plot represents the amplitude of the multiplexed readoutsignal 2630 at each frequency. As shown in the plot, the multiplexedreadout signal 2630 corresponds to a summation of the first qubitreadout signal 2610A, the second qubit readout signal 2610B, and thethird qubit readout frequency signal 2610C. In particular, the examplemultiplexed readout signal 2630 includes a first component centered onthe first readout frequency f1, a second component centered on thesecond readout frequency f2, and a third component centered on the thirdreadout frequency fn. This signal processing scheme can be repeated foreach operating domain of the quantum computing system.

In the example shown, the qubit readout signals from the readout devicesand the multiplexed readout signal 2630 from the multiplexer 2620 areanalog signals. As shown in FIG. 26, the multiplexed readout signal 2630is delivered to the wideband ADC 2640. The wideband ADC 2640 digitizesthe multiplexed readout signal 2630, thus producing a digitized versionof the multiplexed readout signal 2630.

The digital multiplexed readout signal produced by the wideband ADC 2640can be processed, for example, by a classical computer system. Becauseeach qubit readout signal has a distinct readout frequency, the qubitreadout data for each qubit device can be separated out of the digitalmultiplexed readout signal, for example, by digitally de-multiplexingthe signal produced by the wideband ADC 2640. Thus, in the exampleshown, the digital qubit readout data for each qubit device correspondsto the analog qubit readout signal from the qubit device. The qubitreadout data can be used, for example, to identify the quantum states ofthe qubit devices, to generate quantum processor control information, orfor a combination of these and other purposes.

In some implementations, the process 2600 can provide advantages foroperating a quantum computing system. For example, electrical isolationbetween devices in the quantum processor cell can be maintained bydistinct output signal lines for each device in the quantum processorcell. As another example, frequency multiplexing may reduce thefrequency bandwidth allowed through each signal path from the quantumprocessor cell, which may reduce noise. In addition, the frequencyfiltering characteristics may reject out-of-band frequency content,which may provide isolation between devices operating in distinctfrequency bands. Moreover, signal multiplexing can reduce the number ofsignal lines needed to carry signals across temperature stages, whichmay reduce cooling power requirements while also facilitating electricalisolation and noise reduction. In some cases, the process 2600 can beused to obtain a dramatic reduction in cost and complexity of a quantumcomputing system. In some cases, the process 2600 can be used to allow aunit cell of a multi-dimensional device lattice to be reliably repeatedover the lattice, for instance, to build arbitrarily large systems ofinteracting quantum devices.

FIG. 27 is a block diagram showing an example process 2700 fordelivering control signals to a quantum processor cell. For instance,the example process 2700 can be used to deliver control signals for anindividual operating domain of the example quantum computing system 2300shown in FIG. 23A. In some cases, the example process 2700 can be usedto operate a device array that includes a frequency tiling or multiplefrequency sub-arrays, such as, for example, the device array 2120 shownin FIG. 21C, the device array 2220 shown in FIG. 22C, or another devicearray. The example process 2700 can be used, for example, to synthesizeand deliver a time-multiplexed composite control sequence that ischannelized by a switch channelizer for delivery to individual devices(qubit devices, readout devices, coupler devices, etc.) in a quantumprocessor cell.

The block diagram shown in FIG. 27 includes a quantum logic controller2710, a channel controller 2720, a wideband signal synthesizer 2730 withreal-time frequency agility, and a switch 2750. Some aspects of theexample process 2700 may be implemented by the example components shownin FIG. 27, by one or more of the example components shown in FIG. 23A,or by additional or different components. In some implementations of theprocess 2700 shown in FIG. 27, time multiplexing of write/read signalsis performed at a higher temperature (e.g., in a room temperature stageor an intermediate temperature stage), and de-multiplexing of thewrite/read signals is performed at a lower temperature (e.g., in acryogenic temperature stage). The process 2700 may include additional ordifferent operations, and the operations can be performed in the ordershown in FIG. 27 or in another manner.

The example quantum logic controller 2710 receives data from the channelcontroller 2520 and sends instructions to the channel controller 2720.For example, the quantum logic controller 2710 may receive readout dataindicating the states of one or more qubit devices; and the quantumlogic controller 2710 may send instructions corresponding to a quantumlogic operation to be performed by the quantum processor cell. As shownin FIG. 27, the channel controller 2720 composes a digital compositecontrol sequence based on instructions received from the quantum logiccontroller 2710, and the wideband signal synthesizer 2730 generates ananalog composite control sequence based on the digital composite controlsequence received from the channel controller 2720.

In the example shown, the wideband signal synthesizer 2730 generatestime-multiplexed control signals 2740. The time-multiplexed controlsignals 2740 include a write signal 2742A for a first qubit device, awrite signal 2742B for a second qubit device, a read signal 2744A for afirst readout device, and a read signal 2744B for a second readoutdevice. As shown in FIG. 27, each of the respective signals is separatedin the time domain by a switch interval.

In the example shown, the time-multiplexed control signal 2740 isswitched (or channelized) by the switch 2750. On one output channel, theswitch 2750 generates a first series of de-multiplexed control signals2760A; and on another output channel, the switch 2750 generates asecond, distinct series of de-multiplexed control signals 2760B. Thede-multiplexed control signals 2760A include the write signal 2742A forthe first qubit device and the read signal 2744A for the first readoutdevice. The de-multiplexed control signals 2760B include the writesignal 2742B for the second qubit device and the read signal 2744B forthe second readout device.

In the example shown, the write signal 2742A has a first frequency thatis addressed to the first qubit device, which has a first qubitoperating frequency, and the write signal 2742B has a second, distinctfrequency that is addressed to the second qubit device, which has adistinct, second qubit operating frequency. Similarly, the read signal2744A has a first frequency that is addressed to the first readoutdevice, which has a first readout frequency, and the read signal 2744Bhas a second, distinct frequency that is addressed to the second readoutdevice, which has a distinct, second readout frequency.

Aspects of the example technique shown in FIG. 27 can be implemented,for example, by a solid state switch or switched filter bank that isused to implement time-division multiplexing. As shown, the signal foreach device is communicated in a time interval, and the switch iselectronically controlled to provide a continuous signal path to theappropriate output while other signal paths are isolated. In each timeinterval, respective signals (which may have the same or differentcontent) are routed to either the same destination or a differentdestination by modifying the switch state to propagate the signal alongan alternate output signal path.

The example architecture shown in FIG. 27 may provide advantages, insome instances, for controlling a quantum processor cell. For example,the architecture may enable control signals to be delivered by asignificantly smaller number of electronic components and signalchannels. Reducing the number of electronic components can significantlyreduce the cost and complexity of the quantum computing system.Moreover, reducing the number of signal lines can significantly reducethe interface between cryogenic temperature stages and highertemperature stages, which may improve shielding and isolation of thequantum processor cell.

FIG. 28 is a block diagram of an example quantum computing system 2800.The example quantum computing system 2800 can include the features ofthe example quantum computing system 100A shown in FIG. 2, the examplequantum computing system 2300 shown in FIG. 23A, or the example quantumcomputing system 2800 can be implemented in another manner. In someimplementations, the example quantum computing system 2800 can encodeand process information in a device array that includes a frequencytiling or multiple frequency sub-arrays, such as, for example, thedevice array 2120 shown in FIG. 21C, the device array 2220 shown in FIG.22C, or another device array. In some instances, one or more componentsof the quantum computing system 2800 may operate according to theexample techniques shown and described with respect to one or more ofFIGS. 23A, 23B, 24, 25, 26 and 27, or the quantum computing system 2800may operate in another manner.

The example quantum computing system 2800 shown in FIG. 28 includesmultiple operating domains and multiple operating levels. The operatingdomains each include a subset of the qubits in a quantum processor cell,and each operating domain may include dedicated hardware at one or moreof the operating levels of the quantum computing system 2800. In somecases, multiple operating domains share resources at one or more ofoperating levels.

In the example shown, the quantum computing system 2800 includes asystem control level 2801, which is the highest operating level in thesystem. The quantum computing system 2800 also includes a domain controllevel 2802, which is the second-highest operating level in the system.Below the domain control level 2802, the quantum computing system 2800includes a channel control level 2803. The quantum computing system 2800also includes a quantum processor cell level, which is the lowest levelin the system. The quantum processor cell level includes quantumprocessor cell domains 2804 for the operating domains of the quantumcomputing system 2800.

The example system control level 2801 shown in FIG. 28 includes aquantum compiler 2810, a quantum logic controller (QLC) 2812, a clientinterface 2814, a master RF reference 2816 and a domain bus 2805. Asshown in FIG. 28, the quantum compiler 2810, the QLC 2812 and the clientinterface 2814 communicate with each other by exchanging signals on thedomain bus 2805. In some instances, the quantum compiler 2810, the QLC2812 and the client interface 2814 operate together, for example, toperform one or more operations of the example control interface 2305shown in FIG. 23A, one or more operations of the program interface 122in FIG. 2, or other operations. The system control level 2801 mayinclude additional or different components, and the components of asystem control level may operate in the manner described with respect toFIG. 28 or in another manner.

The example domain control level 2802 includes a domain logic controller(DLC) 2820, a non-volatile memory (NVM)/storage 2821, a video randomaccess memory (vRAM) 2822 (e.g., a flash memory), a graphics processingunit accelerator/optimizer (GPU-AO) 2823, a domain data clock 2824 and adomain RF reference 2825. In some cases, the domain control level 2802includes a set of such components, and possibly other components, foreach operating domain of the quantum computing system 2800. In someinstances, components in the domain control level 2802 perform one ormore operations of the example control interface 2305 shown in FIG. 23A,one or more operations of the program interface 122 shown in FIG. 2, orother operations. The domain control level 2802 may include additionalor different components, and the components of a domain control levelmay operate in the manner described with respect to FIG. 28 or inanother manner.

As shown in FIG. 28, the domain RF reference 2825 in the domain controllevel 2802 communicates with the master RF reference 2816. Also as shownin FIG. 28, the NVM 2821, the vRAM 2822, and the GPU-AO 2823 communicatewith each other by exchanging signals on the channel bus 2806. Theexample buses shown in FIG. 28 (e.g., the domain bus 2805, the channelbus 2806) can be implemented, for example, as high-speed serial computerexpansion buses (e.g., a PCIe (Peripheral Component InterconnectExpress)), or other types of bus devices.

The example channel control level 2803 includes multiple domaincontroller blocks 2830. Each domain controller block 2830 includes oneor more channel controllers. The channel controllers in the domaincontroller block 2830 may operate, for example, as the example channelcontroller 2361 shown in FIG. 23B, or the channel controllers mayoperate in another manner. In the example shown in FIG. 28, the domaincontroller block 2830 includes one or more read/write channelcontrollers 2834 and one or more coupler channel controllers 2832. Insome instances, components in the channel control level 2803 perform oneor more operations of the signal generator system 2302 shown in FIG.23A, one or more operations of the signal generator system 120 shown inFIG. 2, or other operations.

The example read/write channel controller 2834 can control the read andwrite operations for a group of qubit devices in the quantum processorcell domain 2804. This domain may include in some instances a group ofdevices, where each device in the group belongs to a differentsub-array, for instance, as described in FIGS. 21A-21C and 22A-22C, orit may be operated in another way. Similarly, the example couplerchannel controller 2832 can control the coupler operations for a groupof coupler devices in the quantum processor cell domain 2804. Theread/write channel controller 2834 and the coupler channel controller2832 can communicate with each other by exchanging signals on thechannel bus 2806. In some instances, the read/write channel controller2834 and the coupler channel controller 2832 can communicate withcomponents in the domain control level 2802 by exchanging signals on thechannel bus 2806. As shown in FIG. 28, the domain controller block 2830can also communicate with (e.g., receive clock signals from) the domaindata clock 2824 and the domain RF reference 2825.

The quantum processor cell domain 2804 includes qubit devices, readoutdevices and coupler devices that are controlled by control signals fromthe domain controller block 2830. The readout devices may also sendqubit readout signals to the domain controller block 2830. The qubitdevices, readout devices and coupler devices can be housed, for example,in an electromagnetic waveguide system or another structure.

The example quantum computing system 2800 can be assembled and deployedin an appropriate operating environment. For superconducting systems,the operating environment can include a cryogenic, low-noise environmentwhere the ambient level of background noise is reduced or minimized atfrequencies relevant to operation of the quantum processor cell. Forexample, a quantum processor cell with qubit devices and readout devicesoperating in the range of 3 GHz to 8 GHz maybe be deployed in anenvironment between 5 mK and 10 mK. In some cases, a quantum processorcell can be deployed at other temperatures (higher or lower). Thetemperature range can be guided, for example, by the formula f=k_(B)T/h,where f indicates the frequency of background noise, k_(B) representsthe Boltzmann constant, T represents temperature in units of Kelvin, andh represents Planck's constant. In some cases, the temperature range forone or more components of the quantum processor cell can be guided byother considerations or formulas. Moreover, in some cases, one or morelevels or components of the quantum computing system 2800 operate inhigher temperature stages.

In some cases, signals are transferred between components of the quantumcomputing system 2800 on transmission lines or other types of signallines. For example, liquid crystal polymer substrates or other types ofmaterials can be used to fabricate high-density, high-isolation,many-channel microwave signal cables. The example quantum computingsystem 2800 shown in FIG. 28 includes signal lines that transfer signalsbetween high and low temperature stages. In some instances, the signallines extending from high to low temperature stages in a cryogenicapparatus can introduce a thermal shunt. Moreover, the cooling power at10 mK may be less than 5 μW, and the signal delivery can be performed inarchitecture with hundreds, thousands or more qubit devices. To reducethe thermal bridging effects of transmission lines carrying DC, radiofrequency, or microwave signals, a single transmission line may be usedin some instances to deliver signals to multiple devices. In some cases,the signal line connects with a solid state switch, a switched filterbank, a power divider, a frequency multiplexer, or another device in thelow temperature stage, and each input signal line bridging thetemperature stage may divide into multiple signal distribution branchesin the lower temperature stage, for example, to communicate withmultiple devices. For instance, the systems and techniques shown anddescribed with respect to FIGS. 23A, 23B, 24, 25, 26 and 27 may be used,or the signal delivery components can be configured in another manner.

In some instances, after the quantum computing system 2800 has beendeployed, the system is characterized. For example, operatingfrequencies of the devices (qubit devices, coupler devices, readoutdevices) in the quantum processor cell, anharmonicities, power levels,and other parameters of the system can be determined. The system deviceparameters can be determined, for example, by a characterization processthat operates over frequency, power, and time ranges that are broaderthan the operational ranges used for quantum computation. Thus, thequantum computing system 2800 may have broad operating capabilities. Insome instances, s-parameters, input impedances, directional coupleroutputs, and phase characteristics can be used in connection withidentifying system parameters during the characterization process.

In some instances, after the system parameters have been determined bythe characterization process, real-time control over the quantumprocessor cell components can be established. In some cases, thisincludes generating, delivering, applying, extracting and processingsignals in connection with the devices in the quantum processor cell.The processed signals can be interpreted and used to conditionsubsequent input pulses, and this process can occur, for example, withina clock cycle of the quantum processor. For instance, a clock cycle canbe the time between application of successive quantum logic gates duringa quantum computation task. During real-time control, the deviceparameters and operating frequencies can be identified (e.g.,periodically or continuously checked), for example, to account forsources of signal drift (e.g., aging, changes in thermal equilibrium,others).

In some instances, after establishing real-time control of the quantumprocessor cell, a quantum computing algorithm may be executed. Thelogical gates and readout operations that realize the quantum computingalgorithm may be interwoven with additional overhead operations that areused to maintain the integrity of the stored quantum information. Forexample, quantum error correction procedures may be implemented tomaintain computational integrity. The quantum computing algorithm andthe quantum error correction procedures can be managed by the QLC 2812.For example, the QLC 2812 can provide instructions for individualchannels and orchestrate real-time control on each individual channelacross the full quantum processor cell. The QLC 2812 can receive,process and send information to the subsystems of the quantum computingsystem 2800, for example, to execute real-time control of the system.

In some instances, the real-time control of the quantum processor cellcan be used as a computational resource. For example, the quantumcomputing system 2800 can communicate with an external device that isused to orchestrate recompiling and partitioning of the calculations tobe performed across multiple processing nodes based on disparateunderlying hardware or computing paradigms.

In the example shown in FIG. 28, the client interface 2814 communicateswith the QLC 2812 and the quantum compiler 2810. In some instances, anapplication that communicates with the client interface 2814 can be alocal application or a remote application that communicates, forexample, over a data network (e.g., the Internet, cellulartelecommunication infrastructure, a virtual private network, etc.) oranother type of communication channel. In some cases, the clientinterface 2814 specifically targets the application to be run on thequantum computing system 2800. In some cases, an external system targetsthe application to be run on the quantum computing system 2800, and theclient interface 2814 does not target applications. For example, thequantum computing system 2800 may act as a node or an obfuscatedaccelerator for a particular task to be performed in a larger system.

The example quantum compiler 2810 can interpret data and instructionsfrom the client interface 2814 and compile them into a series of quantumlogic gates to realize a computational task. In the example shown, theQLC 2812 can control the execution of the quantum computation on thequantum processor cell. For instance, the QLC 2812 can communicate withmultiple DLCs 2820, and each DLC 2820 can orchestrate the operation ofan individual operating domain. For example, each DLC 2820 can be mappedto and responsible for a physical region of the quantum processor cell(e.g., a subset of a full lattice of qubit devices and coupler devices,or another type of physical region).

The example QLC 2812 may receive measurement data and error-matchingcalculations performed at the domain control level 2802. The example QLC2812 can send each DLC 2820 instructions for the application oftime-sequenced or frequency-multiplexed quantum logic or otheroperations (e.g., single-qubit gates, multi-qubit gates, subroutines, acharacterization process, an optimization protocol, measurements, etc.).The QLC 2812 may receive calculation results from error-correctioncalculations across all operating domains; in some implementations, suchcalculations at the domain control level 2802 are restricted to errorswithin a respective operating domain.

The example master RF reference 2816 in the system control level 2801can function as a master clock that generates a master clock signal. Insome cases, the master clock signal can be distributed for timing andsynchronization to each domain in the control system.

In the domain control level 2802, the DLC 2820 communicates with thesystem control level 2801, for example, receiving system-level controlinstructions in the form of time-sequenced quantum logic operations. Theexample DLC 2820 can be responsible for both execution of quantum logicoperations and other types of operations (e.g., characterization,testing, optimization, etc.) in a given operating domain. The exampleDLC 2820 may instruct one or more channels under its operating domain tooperate in either a real-time computing mode or an off-linecharacterization and testing mode. In some cases, the operating mode ofeach channel is independent of the other channels in the quantumcomputing system 2800.

In some implementations, the DLC 2820 can be implemented as a single- ormulti-core processor; as an FPGA or ASIC; or a combination of these andother systems, which may be locally or remotely located. In some cases,for example, when the processing, memory or storage demands on the DLC2820 are significant, the DLC 2820 may be supplemented on the domaincontrol level 2802 with a memory resource such as the vRAM 2822, theGPU-AO 2823, or another resource. For example, the vRAM 2822 or theGPU-AO 2823 can be used to support error correcting calculations,optimization of individual qubit or coupler channels, or otheroperations. The domain control level 2802 may include a solid state orother storage resource. The master clock signal from the system controllevel 2801 can be distributed to each domain in the domain control level2802, and the domain data clock 2824 within each domain can produce adomain clock signal for synchronizing individual channel controllers inthe channel control level 2803.

In some instances, the GPU-AO 2823 can provide additional computationalresources beyond what is required by the quantum processor cell domainto which it is deployed. Additional processing power (e.g., to form ahigh-performance hybrid computing system) may be provided within thequantum computing control system described herein. For example,additional processing nodes may be implemented based on afield-programmable gate array (FPGA), a graphics processing unit (GPU),an application-specific integrated circuit (ASIC), a system-on-a-chip(SOC), a single- or multi-core central processing unit (CPU)-basedprocessor, or another type of data processing apparatus.

In the example channel control level 2803, individual channelcontrollers are deployed. The read/write channel controller 2834 can beused for read/write control (e.g., measurement and operation) of qubitdevices in the quantum processor cell. The coupler channel controller2832 can be used for operation of coupler devices in the quantumprocessor cell. In some cases, the architecture of both types of channelcontrollers can be the same. In some cases, the read/write channelcontroller 2834 can have physical attributes or performancespecifications that are distinct from the attributes or specificationsof the coupler channel controller 2832. For example, the read/writechannel controller 2834 may receive source signals having components inthe range of 3 GHz to 5 GHz for control of qubit devices, and the rangeof 5 GHz to 7 GHz for control of readout devices, and the couplercontrol channel 2832 may receive source signals in the range of DC (zerofrequency) to 1 GHz for control of coupler devices. Other frequencyranges may be used in various implementations.

In some instances, the FPGA of each channel controller is in real-timecommunication with the DLC 2820. At each clock cycle, the FPGA in someor all of the channel controllers in the domain controller block 2830can communicate to the DLC 2820 a status or measurement outcome, and canreceive from the DLC 2820 instruction for subsequent execution. The FPGAmay receive the instructions from the DLC 2820 and induce the DAC andADC within the channel controller to produce or process signals thatallow the system to perform quantum computation operations realizingthose instructions. In some cases, the FPGA can implement Kalman filterdigital signal processing techniques or other types of processes tooptimize or otherwise improve the interpretation of qubit readoutsignals. In some cases, the FPGA, the DAC and the ADC within eachchannel controller operate as described with respect to FIG. 23B, orthey may operate in another manner.

In some implementations, the transition frequencies of the qubit devicesand the quantum processor cell are staged in frequency. For instance,the qubit frequencies can be chosen such that each qubit in the quantumprocessor cell has a qubit operating frequency that is distinct from theoperating frequencies of all nearest-neighbor qubits, and eachnearest-neighbor for any given qubit has a different qubit operatingfrequency difference than the other nearest-neighbors for the givenqubit. Thus, each qubit can have a different difference in frequencybetween itself and each neighboring qubit, such that no two couplerdevices that have the same drive frequency are coupled to the same qubitdevice.

In some instances, each individual channel of the quantum computingsystem (e.g., each channel controller) controls a row, column, sub-arrayor other domain of one or more subsystems of the quantum computingsystem 2800. Subsystems may include any structure or component thatreceives control signals. For example, subsystems may include qubitdevices, where control signals are used for one-qubit gates or encodingan initial state; readout devices, where control signals are used forextracting information or projective quantum measurement; or other typesof devices. In some instances, staging subsystems at differentfrequencies and controlling those subsystems with pulses reduces thetotal number of control channels required in the quantum computingsystem, and may provide other efficiencies or advantages.

In a general aspect of what is described above, a quantum computingmethod includes encoding information in a multi-dimensional array ofqubit devices housed in a multi-dimensional electromagnetic waveguidelattice. The qubit devices have respective qubit operating frequencies.The electromagnetic waveguide lattice is configured to suppress signalpropagation between the qubit devices over a frequency range thatincludes the qubit operating frequencies.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The method caninclude processing the information encoded in the qubit devices byoperation of coupler devices housed in the electromagnetic waveguidelattice between respective pairs of the qubit devices. The method caninclude processing the information encoded in the qubit devices byoperation of qubit devices. The method can include extracting outputinformation from the qubit devices by operation of readout deviceshoused in the quantum processor cell assembly.

In a general aspect of what is described above, a quantum computingsystem includes a quantum processor cell assembly. The quantum processorcell assembly includes an electromagnetic waveguide system. Theelectromagnetic waveguide system includes an interior surface thatdefines an interior volume of intersecting waveguides. The intersectingwaveguides define cutoff frequencies and are configured to evanesceelectromagnetic waves below the cutoff frequencies. The quantumcomputing system includes a multi-dimensional array of qubit deviceshoused in the electromagnetic waveguide system. The qubit devices haverespective qubit operating frequencies below the cutoff frequencies.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The electromagneticwaveguide system can define a two-dimensional waveguide lattice in whicha first subset of the waveguides intersect a second subset of thewaveguides at a two-dimensional array of waveguide intersections, andthe cutoff frequencies are independent of the size of thetwo-dimensional array. The two-dimensional array can include rows andcolumns, and the cutoff frequencies can be independent of the number ofrows and the number of columns. The electromagnetic waveguide system candefine a three-dimensional waveguide lattice in which three distinctsubsets of the waveguides intersect each other at a three-dimensionalarray of waveguide intersections, and the cutoff frequencies can beindependent of the size of the three-dimensional array. Thethree-dimensional array includes rows, columns and layers, and thecutoff frequencies are independent of the number of rows, the number ofcolumns, and the number of layers. The interior surface can definewaveguide cross-sections, and the cutoff frequencies can be defined bythe waveguide cross-sections. The largest dimension of at least one ofthe waveguide cross-sections can be between 0.1 and 1.0 centimeters. Theinterior surface can define waveguide propagation axes that areperpendicular to the respective waveguide cross-sections. Theintersecting waveguides can each be configured to propagateelectromagnetic waves above the cutoff frequency. Each of theintersecting waveguides can define substantially the same cutofffrequency. Each qubit device can include an electronic circuit thatdefines the qubit operating frequency of the qubit device. A firstsubset of the waveguides can intersect a second subset of the waveguidesat a multi-dimensional array of waveguide intersections in the quantumprocessor cell assembly. The quantum computing system can include thequbit devices housed at the waveguide intersections and coupler deviceshoused between neighboring pairs of the qubit devices within the quantumprocessor cell assembly. The quantum computing system can includecoupler devices housed at the waveguide intersections and the qubitdevices housed within the quantum processor cell assembly betweenneighboring pairs of the coupler devices. The multi-dimensional array ofwaveguide intersections can be aligned with the multi-dimensional arrayof qubit devices. The quantum computing system can include readoutdevices housed in the quantum processor cell assembly, the readoutdevices operably coupled to the qubit devices and configured to producequbit readout signals based on electromagnetic interactions with thequbit devices. At least a portion of the interior surface can include asuperconducting material. At least a portion of the interior surface caninclude a metallic conductor material. The quantum processor cellassembly can include a lid component and a base component. The lidcomponent and based component can form a partial enclosure that includesthe interior volume of the intersecting waveguides.

In a general aspect of what is described above, a quantum computingmethod includes receiving qubit control signals at a multi-dimensionalarray of qubit devices in an electromagnetic waveguide system of aquantum processor cell assembly. The qubit devices having respectivequbit operating frequencies. The electromagnetic waveguide system has aninterior surface that defines an interior volume of intersectingwaveguides. Each intersecting waveguide defining a cutoff frequencyabove the qubit operating frequency and is configured to evanesceelectromagnetic waves below the cutoff frequency.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The electromagneticwaveguide system can define apertures through a portion of the interiorsurface, and the qubit control signals can be received over controllines that extend in the apertures and couple the qubit devices with anexternal control system. The quantum computing method can includesupporting the qubit devices in the electromagnetic waveguide system ona signal board disposed in the quantum processor cell assembly. Thesignal board can include qubit signal lines that deliver the qubitcontrol signals to the respective qubit devices. The signal board caninclude a layered structure that includes the signal lines betweenlayers of insulator material. The electromagnetic waveguide system caninclude an interior surface that defines waveguide propagation axes andwaveguide cross-sections perpendicular to the waveguide propagationaxes. The cutoff frequencies can be defined by the waveguidecross-sections. Each qubit device can include an electronic circuit thatdefines the qubit operating frequency. The electromagnetic waveguidesystem can defines a two-dimensional waveguide lattice in which a firstsubset of the waveguides are parallel to each other, a second subset ofthe waveguides are parallel to each other, and the first subsetintersect the second subset at a two-dimensional array of waveguideintersections. The electromagnetic waveguide system can defines athree-dimensional waveguide lattice in which a first subset of thewaveguides are parallel to each other, a second subset of the waveguidesare parallel to each other, a third subset of the waveguides areparallel to each other, and the first, second and third subsetsintersect each other at a three-dimensional array of waveguideintersections. The multi-dimensional array of waveguide intersectionscan be aligned with the multi-dimensional array of qubit devices.Receiving the qubit control signals can cause the qubit devices toprocess information encoded in the qubit devices. The quantum computingmethod can include receiving coupler control signals at coupler devicehoused between neighboring pairs of the qubit devices in theelectromagnetic waveguide system. The quantum computing method caninclude producing qubit readout signal at readout devices that arehoused in the electromagnetic waveguide system and coupled to the qubitdevices, the qubit readout signals produced in response to readoutcontrol signals delivered to the readout devices.

In a general aspect of what is described above, a quantum computingsystem includes a quantum processor cell assembly comprising a system ofintersecting waveguides. Each of the waveguides defines a cross-sectionand a propagation axis perpendicular to the cross-section, and thecross-section of each waveguide defines a cutoff frequency of thewaveguide. The quantum computing system includes a multi-dimensionalarray of qubit devices housed in the system of intersecting waveguides.The qubit devices have respective qubit operating frequencies below thecutoff frequencies of the intersecting waveguides.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The waveguides caneach define substantially the same cutoff frequency, and each waveguidecan be configured to propagate electromagnetic waves above the cutofffrequency and to evanesce waves below the cutoff frequency. Each qubitdevice can include an electronic circuit that defines the qubitoperating frequency of the qubit device. The qubit devices housed in thesystem of intersecting waveguides can have respective qubit operatingfrequencies below the cutoff frequencies of the intersecting waveguides.Coupler devices can be housed in the system of intersecting waveguidesbetween respective pairs of the qubit devices. The coupler devices canhave coupler operating frequencies below the cutoff frequencies of theintersecting waveguides.

In a general aspect of what is described above, a quantum computingsystem includes a quantum processor cell assembly that includes anelectromagnetic waveguide system. The electromagnetic waveguide systemhas an interior surface that defines an interior volume of intersectingwaveguides. A first subset of the waveguides intersect a second subsetof the waveguides at a multi-dimensional array of waveguideintersections in the quantum processor cell assembly. The waveguideintersections include portions of the interior volume that are sharedbetween the first subset and the second subset. The quantum computingsystem includes a multi-dimensional array of qubit devices housed in theelectromagnetic waveguide system.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The multi-dimensionalarray of waveguide intersections defines distances between neighboringpairs of the waveguide intersections, and the distances can be between0.2 and 2.0 centimeters. The quantum processor cell assembly can includea lid component and a base component. The lid component and basedcomponent can form a partial enclosure that includes the interior volumeof the intersecting waveguides. The lid component can include a firstportion of the interior surface, and the base component can include asecond portion of the interior surface. At least a portion of theinterior surface can be a superconducting material. At least a portionof the interior surface can be a metallic conductor material. Theelectromagnetic waveguide system can define apertures through a portionof the interior surface about the waveguide intersections. The quantumcomputing system can include control lines that couple the qubit deviceswith an external control system, and the control lines can extend in theapertures. The electromagnetic waveguide system can include atwo-dimensional waveguide lattice in which the first subset ofwaveguides are parallel to each other and the second subset ofwaveguides are parallel to each other. The first subset of waveguidescan be perpendicular to the second subset of waveguides, and the firstsubset can intersect the second subset at right angles in the quantumprocessor cell assembly. Each of the waveguides can include at least onesubsection that has a substantially rectangular cross-section. Thecross-section can be defined by opposing right and left sidewalls of theelectromagnetic waveguide system. The rectangular cross-section can bepartially defined by opposing upper and lower sidewalls of theelectromagnetic waveguide system. At each waveguide intersection, theright and left sidewalls of a waveguide in the first subset can meet theright and left sidewalls of a waveguide in the second subset. Theinterior surface can include sidewalls made of at least one of metallicconducting material or superconducting material. The quantum computingsystem can include qubit devices housed at the waveguide intersectionsand coupler devices housed in the electromagnetic waveguide systembetween respective pairs of the qubit devices. The quantum computingsystem can include coupler devices housed at the waveguide intersectionsand qubit devices housed in the electromagnetic waveguide system betweenrespective pairs of the coupler devices. The quantum computing systemcan include a signal board disposed in the quantum processor cellassembly. The signal board can support the qubit devices in theelectromagnetic waveguide system. The signal board can include qubitsignal lines configured to deliver qubit control signals to therespective qubit devices. The signal board can be a layered structurethat includes the signal lines between layers of insulator material. Thesignal board can support coupler devices in the electromagneticwaveguide system. The coupler devices can reside between respectivepairs of qubit devices. The signal board can include receptacles thatsupport the qubit devices and the coupler devices and arms that supportthe receptacles. One or more of the arms can extend through a wall ofthe electromagnetic waveguide system between an interior and an exteriorof the electromagnetic waveguide system. The signal board can includecoupler signal lines configured to deliver coupler control signals tothe coupler devices. The signal board can support each qubit device at arespective waveguide intersection, and the multi-dimensional array ofqubit devices can be aligned with the multi-dimensional array ofwaveguide intersections. The quantum computing system can include aninput interconnect system that includes plateau structures. The plateaustructures can include input interconnect signal lines that deliverdevice control signals to the signal board. The quantum computing systemcan include an output interconnect system that includes plateaustructures. The plateau structures can include output interconnectsignal lines that transfer qubit readout signals from the signal board.The intersecting waveguides can define cutoff frequencies. Eachwaveguide can be configured to evanesce electromagnetic waves below thecutoff frequency of the waveguide. The cutoff frequencies can be definedby respective cross-sections of the waveguides and they can beindependent of the size of the multi-dimensional array.

In a general aspect of what is described above, a quantum computingmethod includes receiving qubit control signals at qubit devices housedin an electromagnetic waveguide system of a quantum processor cellassembly. The electromagnetic waveguide system includes an interiorsurface that defines an interior volume of intersecting waveguides. Afirst subset of the waveguides intersect a second subset of thewaveguides at a multi-dimensional array of waveguide intersections inthe quantum processor cell assembly. The waveguide intersections includeportions of the interior volume that are shared between the first subsetand the second subset.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The quantum computingmethod includes receiving coupler control signals at coupler deviceshoused between neighboring pairs of the qubit devices in theelectromagnetic waveguide system. Receiving the coupler control signalsat the coupler devices can cause the coupler devices to produceelectromagnetic interactions between the neighboring pairs of qubitdevices. The quantum computing method includes producing qubit readoutsignals at readout devices that are housed in the electromagneticwaveguide system. The qubit readout signals can be produced in responseto readout control signals delivered to the readout devices.

In a general aspect of what is described above, a method includesforming a multi-dimensional lattice of intersecting waveguides in aquantum processor cell assembly. A first subset of the waveguidesintersect a second subset of the waveguides at a multi-dimensional arrayof waveguide intersections in the quantum processor cell assembly. Thewaveguide intersections include interior volumes that are shared betweenthe first subset and the second subset. The method includes supporting amulti-dimensional array of qubit devices in the lattice of intersectingwaveguides.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. Forming theintersecting waveguides can include assembling an upper cell member to alower cell member. The upper and lower cell members can include interiorsurface structures that define an interior volume of the intersectingwaveguides. The qubit devices can be supported between the assembledupper and lower cell assembly members. The qubit devices can besupported by a signal board disposed between the upper and lower cellmembers. The signal board can include receptacles for the respectivequbit devices and arms that support the receptacles. At least a portionof the arms can extend through a wall that separates an interior and anexterior of the intersecting waveguides. The interior surface structurescan include sidewalls that define cross-sections of the intersectingwaveguides. The qubit devices can be supported at the waveguideintersections. The method can include supporting coupler devices betweenneighboring pairs of the qubit devices within the intersectingwaveguides. The method can include supporting coupler devices in theintersecting waveguides at the waveguide intersections. The qubitdevices can be supported between respective pairs of the couplerdevices. The method can include supporting readout devices in thequantum processor cell assembly. The method includes aligning themulti-dimensional array of qubit devices with the multi-dimensionalarray of waveguide intersections.

In a general aspect of what is described above, a quantum computingsystem includes qubit devices housed in a quantum processor cellassembly. The qubit devices have respective qubit operating frequencies.The quantum computing system includes an electromagnetic waveguidesystem in the quantum processor cell assembly. The electromagneticwaveguide system includes waveguide structures between neighboring pairsof the qubit devices. The waveguide structures are configured tosuppress signal propagation in a frequency range that includes the qubitoperating frequencies. The quantum computing system includes couplerdevices housed in the quantum processor cell assembly betweenneighboring pairs of the qubit devices. The coupler devices areconfigured to selectively couple the respective neighboring pairs ofqubit devices based on coupler control signals received from a controlsource external to the quantum processor cell assembly.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The quantum computingsystem can include readout devices housed in the quantum processor cellassembly. The readout devices can be operably coupled to the qubitdevices and configured to produce qubit readout signals based onelectromagnetic interactions with the qubit devices. The quantumcomputing system can include a signal board that supports the qubitdevices and the coupler devices in the quantum processor cell assembly.The signal board can include receptacles that support the qubit devicesand the coupler devices and arms that support the receptacles. One ormore of the arms can include qubit signal lines that are configured tocommunicate qubit control signals to the qubit devices from an inputsignal processing system. One or more of the arms can include couplersignal lines that are configured to communicate coupler control signalsto the qubit devices from an input signal processing system. One or moreof the arms can extend through a wall of the electromagnetic waveguidesystem between an interior and an exterior of the electromagneticwaveguide system. The quantum computing system includes an inputinterconnect system that includes plateau structures. The plateaustructures include input interconnect signal lines that deliver devicecontrol signals to the signal board. The quantum computing systemincludes an output interconnect system that includes plateau structures.The plateau structures include output interconnect signal lines thattransfer qubit readout signals from the signal board. The waveguidestructures can be made of superconducting material, metallic conductormaterial, or a combination. The coupler control signals can be receivedover a control line that extends through an aperture in theelectromagnetic waveguide system. The electromagnetic waveguide systemcan include an interior surface that defines an interior volume ofintersecting waveguides, and each waveguide structure can be asubsection of one of the intersecting waveguides. The electromagneticwaveguide system can include a two-dimensional waveguide lattice thatincludes a first subset of waveguides intersecting a second subset ofthe waveguides at a two-dimensional array of waveguide intersections inthe quantum processor cell assembly. The two-dimensional waveguidelattice can include waveguide subsections between the waveguideintersections, and each subsection can be configured to suppress signalpropagation at one or more qubit operating frequencies. The qubitdevices can be housed at the waveguide intersections, and the couplerdevices can be housed between the qubit devices. The coupler devices canbe housed at the waveguide intersections, and the qubit devices can behoused between the coupler devices. The electromagnetic waveguide systemcan include a three-dimensional waveguide lattice that includes threedistinct subsets of the waveguides intersecting each other at athree-dimensional array of waveguide intersections in the quantumprocessor cell assembly. The three-dimensional waveguide lattice caninclude waveguide subsections between the waveguide intersections, andeach subsection can be configured to suppress signal propagation at oneor more qubit operating frequencies. The waveguide structures can definecutoff frequencies, and they can be configured to evanesceelectromagnetic waves below the cutoff frequencies. The qubit operatingfrequencies can be below the cutoff frequencies, and the coupler devicescan have coupler operating frequencies below the cutoff frequencies. Thequbit devices can be transmon devices, and the coupler devices can befluxonium devices.

In a general aspect of what is described above, a quantum computingmethod includes receiving, at a coupler device in a quantum processorcell assembly, a coupler control signal from a control source externalto the quantum processor cell assembly. The coupler device is housedbetween qubit devices that have respective qubit operating frequencies.The coupler control signal causes the coupler device to produce anelectromagnetic interaction between the qubit devices. The quantumcomputing method includes suppressing, by a waveguide structure betweenthe qubit devices, signal propagation in a frequency range that includesthe qubit operating frequencies.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. Each qubit device caninclude an electronic circuit that defines the qubit operating frequencyof the qubit device. The quantum computing method can include receivinga qubit control signal at one of the qubit devices. The qubit controlsignal can cause the qubit device to process information encoded in thequbit device. The quantum computing method can include producing qubitreadout signals by operation of readout devices housed in the processorcell assembly. The qubit readout signals can be produced in response toreadout control signals delivered to the readout devices based oninteractions between the readout devices and the qubit devices. A_(n)electromagnetic waveguide system can include an interior surface thatdefines an interior volume of intersecting waveguides. The waveguidestructure that suppresses propagation of signals can be a subsection ofelectromagnetic waveguide system. The quantum computing method caninclude receiving qubit control signals at qubit devices housed in anelectromagnetic waveguide system in the quantum processor cell assembly.The quantum computing method can include receiving coupler controlsignals at coupler devices housed between respective pairs of the qubitdevices in the electromagnetic waveguide system. The electromagneticwaveguide system can include a two-dimensional waveguide lattice thatincludes a first subset of waveguides intersecting a second subset ofwaveguides at waveguide intersections in the quantum processor cellassembly. The qubit devices and coupler devices can be arranged inalignment with the two-dimensional waveguide lattice. The quantumcomputing method can include suppressing signal propagation at one ormore qubit operating frequencies by operation of the electromagneticwaveguide system.

In a general aspect of what is described above, a quantum computingsystem includes a quantum processor cell that includes qubit chips,coupler chips and a signal board. Each qubit chip includes a qubitdevice. Each coupler chip includes a coupler device. The signal boardsupports the qubit chips and the coupler chips within the quantumprocessor cell. The qubit chips are arranged in a multi-dimensionalarray of qubit locations. The coupler chips are arranged betweenneighboring pairs of the qubit chips in the multi-dimensional array.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The quantum processorcell can include an electromagnetic waveguide system, and the signalboard supports the qubit chips and the coupler chips within theelectromagnetic waveguide system. The signal board can includereceptacles that support the qubit devices and the coupler devices andarms that support the receptacles. One or more of the arms can extendthrough a wall of the electromagnetic waveguide system between aninterior and an exterior of the electromagnetic waveguide system. Thesignal board can include qubit signal lines that deliver the qubitcontrol signals to the respective qubit devices. The signal board caninclude coupler signal lines that deliver the coupler control signals tothe respective coupler devices. The signal board can be a layeredstructure that includes signal lines between layers of insulatormaterial.

In a general aspect of what is described above, a quantum computingsystem includes a quantum processor cell that houses qubit devices andcoupler devices in an electromagnetic waveguide system. The qubitdevices and the coupler devices form a multi-dimensional device latticecomprising multiple adjoining unit cells. Each unit cell of the devicelattice includes at least one of the qubit devices and at least one ofthe coupler devices. The quantum computing system includes a controlsystem communicably coupled to the quantum processor cell. The controlsystem is configured to control the qubit devices.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The quantum processorcell can house readout devices, and each unit cell of the lattice caninclude at least one of the readout devices. The electromagneticwaveguide system can include a multi-dimensional waveguide latticeformed by intersecting waveguide sections, and the device lattice can bealigned in the waveguide lattice. The multi-dimensional device latticecan be a two-dimensional device lattice, and each unit cell can includetwo or more coupler devices. The multi-dimensional device lattice can bea three-dimensional device lattice, and each unit cell can include threeor more coupler devices. The quantum computing system can include asignal delivery system that communicates signals between the controlsystem and the quantum processor cell.

In a general aspect of what is described above, a quantum computingsystem includes a multi-dimensional array of qubit devices. Each qubitdevice has a respective qubit operating frequency that is independent ofan offset electromagnetic field experienced by the qubit device. Thequantum computing system includes coupler devices residing at intervalsbetween neighboring pairs of the qubit devices in the multi-dimensionalarray. Each coupler device is configured to produce an electromagneticinteraction between the respective neighboring pair of qubit devices.Each coupler device configured to vary a coupling strength of theelectromagnetic interaction according to an offset electromagnetic fieldexperienced by the coupler device.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The quantum computingsystem includes readout devices associated with the multi-dimensionalarray of qubit devices. Each readout device can be operably coupled to asingle, respective qubit device and configured to produce a qubitreadout signal that indicates a state of the respective qubit device.The qubit readout signal can be produced in response to a readoutcontrol signal delivered to the readout device. Each qubit device canhave two or more nearest-neighbor qubit devices in the multi-dimensionalarray. The qubit operating frequency of each qubit device can bedistinct from the respective qubit operating frequencies of eachnearest-neighbor qubit device. Each of the neighboring pairs of qubitdevices can include a first qubit device having a first qubit operatingfrequency and a second qubit device having a second, distinct qubitoperating frequency. Each coupler device can have a respective coupleroperating frequency that varies with the offset electromagnetic fieldexperienced by the coupler device, and the coupling strength can varyaccording to the coupler operating frequency. The coupler device betweeneach neighboring pair of qubit devices can include bias circuitry andcoupler circuitry. The bias circuitry can be configured to produce anoffset electromagnetic field that tunes the coupler operating frequencyof the coupler device. The coupler circuitry can be configured toexperience the offset electromagnetic field and produce theelectromagnetic interaction between the neighboring pair of qubitdevices. In the coupler device between each neighboring pair of qubitdevices the bias circuitry can be configured to tune the coupleroperating frequency to a frequency range associated with at least one ofthe first qubit operating frequency or the second qubit operatingfrequency. The coupler circuitry can be configured to produce theelectromagnetic interaction between the neighboring pair of qubitdevices by resonating at a drive frequency that corresponds to a sum ordifference of the first qubit operating frequency and the second qubitoperating frequency. Each of the qubit devices can be a member of atleast two of the neighboring pairs of the qubit devices in themulti-dimensional array. The multi-dimensional array can defines a firstset of intervals along a first dimension of the array and a second setof intervals along a second dimension of the array. A first subset ofthe coupler devices can reside at the first set of intervals, and asecond subset of the coupler devices can reside at the second set ofintervals. The multi-dimensional array can be a two-dimensional array,and the qubit devices can define rows and columns of the two-dimensionalarray. The coupler devices can reside at intervals between the qubitdevices along the rows and columns of the two-dimensional array. Therows of the two-dimensional array can be oriented perpendicular to thecolumns of the two-dimensional array. The two-dimensional array can be asquare array, a rectangular array, or another type of rectilinear array.The multi-dimensional array can be a three-dimensional array. The qubitdevices can define rows, columns and layers of the three-dimensionalarray. The three-dimensional array can be a rectilinear array. Each ofthe qubit devices can be a charge qubit. Each of the qubit devices canbe a transmon qubit. Each of the qubit devices can be a flux qubit. Eachof the qubit devices can be a fluxonium qubit. Each fluxonium qubit caninclude a topologically closed capacitance. The quantum computing systemcan include an electromagnetic waveguide system. The electromagneticwaveguide system can have an interior surface that defines an interiorvolume of intersecting waveguides. The qubit devices can be housed inthe electromagnetic waveguide system. The intersecting waveguides candefine cutoff frequencies and can be configured to evanesceelectromagnetic waves below the cutoff frequencies. The qubit operatingfrequency of each qubit device can be below the cutoff frequencies. Theinterior surface of the electromagnetic waveguide system can definewaveguide cross-sections. The cutoff frequencies can be defined by thewaveguide cross-sections. A first subset of the waveguides can intersecta second subset of the waveguides at an array of waveguide intersectionsin the electromagnetic waveguide system. The waveguide intersections caninclude portions of the interior volume that are shared between thefirst subset and the second subset. The qubit devices can be housed atthe waveguide intersections. The coupler devices can be housed in theelectromagnetic waveguide system between the intersections. Themulti-dimensional array of qubit devices defines distances betweenneighboring pairs of the qubit devices, and the distances can be between0.2 and 2.0 centimeters. Each coupler device can be operatively coupledto a single respective neighboring pair of the qubit devices. Eachneighboring pair of the qubit devices can be operatively coupled by asingle respective coupler device. Each coupler device can be configuredto produce the electromagnetic interaction based on coupler controlsignals that include AC and DC components.

In a general aspect of what is described above, a quantum computingmethod includes receiving qubit control signals in a multi-dimensionalarray of qubit devices. Each qubit device has a respective qubitoperating frequency that is independent of an offset electromagneticfield experienced by the qubit device. The qubit control signal receivedby each qubit device is configured to manipulate a quantum state of thequbit device. The quantum computing method includes receiving couplercontrol signals at coupler devices. The coupler devices reside atintervals between neighboring pairs of the qubit devices in themulti-dimensional array. The coupler control signal received by eachcoupler device is configured to produce an electromagnetic interactionbetween the neighboring pair of qubit devices that the coupler deviceresides between. A coupling strength of the electromagnetic interactionproduced by each coupler device is influenced by an offsetelectromagnetic field experienced by the coupler device.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. Each qubit controlsignal can include a microwave pulse. Each qubit control signal can beconfigured to execute a single-qubit gate on qubit device that receivesthe qubit control signal. A component of the coupler control signals canbe a DC signal that causes the coupler devices to experience offsetelectromagnetic fields. Each of the coupler devices can has a respectivecoupler operating frequency that varies with the offset electromagneticfield experienced by the coupler device. The coupling strength can varyaccording to the coupler operating frequency. Each of the neighboringpairs of qubit devices can include a first qubit device having a firstqubit operating frequency and a second qubit device having a second,distinct qubit operating frequency. The offset electromagnetic fieldexperienced by each coupler device can tunes the coupler device to afrequency range associated with at least one of the first qubitoperating frequency or the second qubit operating frequency. A componentof the coupler control signals can be an AC signal that drives thecoupler devices while the coupler operating frequencies are tuned to therespective frequency ranges. Each control device can be driven at adrive frequency that corresponds to a sum or difference of the firstqubit operating frequency and the second qubit operating frequency. Eachcoupler control signal can be configured to execute a two-qubit gate onthe respective pair of qubit devices that the coupler device residesbetween. Each qubit device can have two or more nearest-neighbor qubitdevices in the multi-dimensional array. The qubit operating frequency ofeach qubit device can be distinct from the respective qubit operatingfrequencies of each of its nearest-neighbor qubit device. Each of theneighboring pairs of qubit devices can include a first qubit devicehaving a first qubit operating frequency and a second qubit devicehaving a second, distinct qubit operating frequency. The quantumcomputing method can include producing qubit readout signals byoperation of readout devices associated with the multi-dimensional arrayof qubit devices. Each readout device can be operably coupled to asingle, respective qubit device. Each qubit readout signal can beproduced by one of the readout devices in response to a readout controlsignal. The qubit readout signal can be produced based on anelectromagnetic interaction between the readout device and therespective qubit device. The quantum computing method can includereceiving readout control signals at the readout devices. Each readoutcontrol signal can be received by a respective readout device. Eachqubit readout signal can be produced by a respective readout device inresponse to the readout control signal received by the respectivereadout device. Each coupler device can be operatively coupled to asingle respective neighboring pair of the qubit devices. Each couplerdevice can be configured to produce the electromagnetic field based oncoupler control signals that include AC and DC components.

In a general aspect of what is described above, a quantum computingsystem includes a multi-dimensional array of qubit devices. Each qubitdevice has a respective qubit operating frequency that is independent ofan offset electromagnetic field experienced by the qubit device. Thequantum computing system includes readout devices associated with themulti-dimensional array of qubit devices. Each readout device isoperably coupled to a single, respective qubit device and configured toproduce a qubit readout signal that indicates a state of the respectivequbit device.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The qubit devices canhave respective qubit operating frequencies in a first frequency band,and the readout devices can respective readout frequencies in a second,separate frequency band. The qubit devices can have respective qubitoperating frequencies in a frequency band, and the readout devices canhave respective readout frequencies that are interleaved between thequbit operating frequencies in the frequency band. Each qubit device canhave two or more nearest-neighbor qubit devices in the multi-dimensionalarray. The qubit operating frequency of each qubit device can bedistinct from the respective qubit operating frequencies of each of itsnearest-neighbor qubit device. Each readout device can have a respectivereadout frequency and two or more nearest-neighbor readout devices. Thereadout frequency of each readout device can be distinct from therespective readout frequencies of each nearest-neighbor readout device.The quantum computing system can include coupler devices residing atintervals between neighboring pairs of the qubit devices in themulti-dimensional array. Each coupler device can be configured toproduce an electromagnetic interaction between the respectiveneighboring pair of qubit devices that the coupler device residesbetween. A coupling strength of the electromagnetic interaction producedby each coupler device can vary with an offset electromagnetic fieldexperienced by the coupler device. The multi-dimensional array can be atwo-dimensional array, and the qubit devices can define rows and columnsof the two-dimensional array. The rows of the two-dimensional array canbe oriented perpendicular to the columns of the two-dimensional array.The two-dimensional array can be a rectilinear array (e.g., a squarearray, a rectangular array). The multi-dimensional array can be athree-dimensional array, and the qubit devices can define rows, columnsand layers of the three-dimensional array. The three-dimensional arraycan be a rectilinear array. Each of the qubit devices can be a chargequbit. Each of the qubit devices can be a transmon qubit. Each of thereadout devices can be capacitively coupled to the single, respectivequbit device. The quantum computing system can include device chips thateach include one of the readout devices and the respective qubit devicethat the readout device is coupled to. The quantum computing system caninclude readout chips and separate qubit chips. Each readout chip caninclude one of the readout devices, and each qubit chip can include oneof the qubit devices. The quantum computing system can include anelectromagnetic waveguide system. The electromagnetic waveguide systemcan have an interior surface that defines an interior volume ofintersecting waveguides. The qubit devices can be housed in theelectromagnetic waveguide system. The intersecting waveguides can eachdefine a cutoff frequency and be configured to evanesce electromagneticwaves below the cutoff frequency. The qubit operating frequency of eachqubit device can be below the cutoff frequencies. The interior surfacecan define waveguide cross-sections, and the cutoff frequencies can bedefined by the waveguide cross-sections.

In a general aspect of what is described above, a quantum computingmethod includes receiving qubit control signals in a multi-dimensionalarray of qubit devices. Each qubit device has a respective qubitoperating frequency that is independent of an offset electromagneticfield experienced by the qubit device. The qubit control signal receivedby each qubit device is configured to manipulate a quantum state of thequbit device. The method includes producing qubit readout signals atreadout devices associated with the multi-dimensional array of qubitdevices. Each readout device is operably coupled to a single, respectivequbit device. Each qubit readout signal is produced by one of thereadout devices based on an electromagnetic interaction between thereadout device and the respective qubit device.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The qubit devices canhave respective qubit operating frequencies in a first frequency band,and the readout devices can have respective readout frequencies in asecond, separate frequency band. The qubit devices can have respectivequbit operating frequencies in a frequency band, and the readout devicescan have respective readout frequencies that are interleaved between thequbit operating frequencies in the frequency band. Each qubit device canhave two or more nearest-neighbor qubit devices in the multi-dimensionalarray, and the qubit operating frequency of each qubit device can bedistinct from the respective qubit operating frequencies of eachnearest-neighbor qubit device. Each readout device can have two or morenearest-neighbor readout devices, and a readout frequency of eachreadout device can be distinct from respective readout frequencies ofeach nearest-neighbor readout device. The quantum computing method caninclude receiving coupler control signals at coupler devices. Thecoupler devices can reside at intervals between neighboring pairs of thequbit devices in the multi-dimensional array. The coupler control signalreceived by each coupler device can be configured to produce anelectromagnetic interaction between the neighboring pair of qubitdevices that the coupler device resides between. The quantum computingmethod can include manipulating coupling strengths of theelectromagnetic interactions produced by the respective coupler devicesby controlling offset electromagnetic fields experienced by therespective coupler devices. Each qubit control signal can include amicrowave pulse. Each qubit control signal can be configured to executea single-qubit gate on a qubit device that receives the qubit controlsignal. The quantum computing method can include receiving readoutcontrol signals at the readout devices. Each readout control signal canbe received by a respective readout device, and each qubit readoutsignal can be produced by a respective readout device in response to thereadout control signal received by the respective readout device. Thequbit readout signal produced by each readout device can be influencedby a quantum state of the qubit device that the readout device isoperably coupled to. Each of the readout devices can be capacitivelycoupled to the single, respective qubit device.

In a general aspect of what is described above, a quantum computingsystem includes a quantum processor cell. The quantum processor cellincludes a multi-dimensional array of qubit devices. Themulti-dimensional array includes sub-arrays associated with separatefrequency bands. The qubit devices in each sub-array have a qubitoperating frequency within the frequency band associated with thesub-array. The quantum computing system includes a signal deliverysystem communicably coupled between the quantum processor cell and acontrol system. The signal delivery system is configured to transfersignals between the array of qubit devices and the control system.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The frequency bandscan be spaced apart from each other by intervals along a frequencyspectrum. At least one of the frequency bands can be spaced by a firstinterval from the nearest-neighbor frequency band in a first directionin the frequency spectrum, and the same frequency band can be spaced bya second, distinct interval from the nearest-neighbor frequency band ina second direction in the frequency spectrum. The frequency bands can bespaced apart from each other by intervals along a frequency spectrum,and the intervals between neighboring pairs of frequency bands caninclude a first subset of equal intervals and a second subset of equalintervals. The intervals in the first subset can be larger than theintervals in the second subset. The multi-dimensional array can includegroups of the qubit devices. Each group can include one qubit device ineach of the sub-arrays. The groups can collectively define a tiling overthe multi-dimensional array. The multi-dimensional array can be atwo-dimensional array, and the tiling can be a two-dimensional tiling.Each group can consist of six qubit devices, and the tiling can be asix-by-six tiling. Each group can consist of five qubit devices, and thetiling can be a five-by-five tiling. The control system can include oneor more waveform generator systems configured to generate multiplexedcontrol signals for each respective group of the qubit devices. Thesignal delivery system can include an input signal processing systemthat includes, for each group of qubit devices, an input channel, ade-multiplexer and output channels. The input channel can be configuredto receive the multiplexed control signal for the group of qubitdevices. The de-multiplexer can be configured to separate device controlsignals from the multiplexed control signal for the group of qubitdevices. The output channels can be configured to communicate therespective device control signals into the quantum processor cell forthe group of qubit devices. The signal delivery system can include anoutput signal processing system that includes, for each group of qubitdevices, input channels, a multiplexer and an output channel. The inputchannels can be configured to receive qubit readout signals from a groupof readout devices associated with the group of qubit devices. Themultiplexer can be configured to generate a multiplexed readout signalby multiplexing the qubit readout signals. The output channel can beconfigured to communicate the multiplexed readout signal from the outputsignal processing system on a physical channel. The control system caninclude one or more data processors. The data processors can be operableto receive the multiplexed readout signal for each group of readoutdevices. The data processors can be operable to identify, from eachmultiplexed readout signal, qubit readout data for each qubit device inthe group based on the readout frequency of the associated readoutdevice. Each qubit device can have two or more nearest-neighbor qubitdevices in the multi-dimensional array, and the qubit operatingfrequency of each qubit device can be distinct from the respective qubitoperating frequencies of each nearest-neighbor qubit device. The quantumcomputing system can include readout devices associated with themulti-dimensional array of qubit devices. Each readout device can beoperably coupled to a single, respective qubit device and configured toproduce a qubit readout signal that indicates a state of the respectivequbit device. The quantum computing system can include coupler devicesresiding at intervals between neighboring pairs of the qubit devices inthe multi-dimensional array. Each coupler device can be configured toproduce an electromagnetic interaction between the respectiveneighboring pair of qubit devices that the coupler device residesbetween. The electromagnetic interaction produced by each coupler devicecan have a coupling strength that varies with an offset electromagneticfield experienced by the coupler device. Each neighboring pair of qubitdevices can include a first qubit device having a first qubit operatingfrequency and a second qubit device having a second, distinct qubitoperating frequency. The multi-dimensional array can defines a first setof intervals along a first dimension of the array and a second set ofintervals along a second dimension of the array. A first subset of thecoupler devices can reside at the first set of intervals, and a secondsubset of the coupler devices can reside at the second set of intervals.Each of the qubit devices can be a charge qubit. Each of the qubitdevices can be a transmon device. The quantum computing system caninclude an electromagnetic waveguide system. The electromagneticwaveguide system can have an interior surface that defines an interiorvolume of intersecting waveguides. The qubit devices can be housed inthe electromagnetic waveguide system. The intersecting waveguides caneach define a cutoff frequency and be configured to evanesceelectromagnetic waves below the cutoff frequency. The qubit operatingfrequency of each qubit device can be below the cutoff frequencies. Theinterior surface can defines waveguide cross-sections, and the cutofffrequencies can be defined by the waveguide cross-sections.

In a general aspect of what is described above, a quantum computingmethod includes receiving qubit control signals at a quantum processorcell comprising a multi-dimensional array of qubit devices. Themulti-dimensional array includes sub-arrays associated with separatefrequency bands. The qubit devices in each sub-array have a qubitoperating frequency within the frequency band associated with thesub-array. The qubit control signal received by each qubit device isconfigured to manipulate a quantum state of the qubit device. Thequantum computing method includes communicating the qubit controlsignals to respective qubit devices in the quantum processor cell.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The frequency bandscan be spaced apart from each other at intervals along a frequencyspectrum. At least one of the frequency bands is spaced by a firstinterval from the nearest-neighbor frequency band in a first directionin the frequency spectrum, and is spaced by a second, distinct intervalfrom the nearest-neighbor frequency band in a second direction in thefrequency spectrum. The intervals between neighboring pairs of frequencybands can include a first subset of equal intervals and a second subsetof equal intervals. The intervals in the first subset can be larger thanthe intervals in the second subset. The multi-dimensional array caninclude groups of the qubit devices. Each group includes one qubitdevice in each of the sub-arrays. The groups can collectively define atiling over the multi-dimensional array. The multi-dimensional array canbe a two-dimensional array, and the tiling can be a two-dimensionaltiling. The quantum computing method can include, for each respectivegroup of the qubit devices: generating qubit control information;generating a multiplexed control signal from the qubit controlinformation; communicating the multiplexed control signal on a physicalchannel into an input signal processing system; separating qubit controlsignals from the multiplexed control signal by de-multiplexing themultiplexed control signal in the input signal processing system; andcommunicating the respective qubit control signals into the quantumprocessor cell. The quantum computing method can include, for eachrespective group of the qubit devices: producing qubit readout signalsby operating a group of readout devices associated with the group ofqubit devices; generating a multiplexed readout signal in an outputsignal processing system by multiplexing the qubit readout signals;communicating the multiplexed readout signal from the output signalprocessing system on a physical channel; receiving the multiplexedreadout signal at a control system; and identifying, by operation of thecontrol system, qubit readout data for each device in the group, thequbit readout data from each respective readout device identified fromthe multiplexed readout signal based on the readout frequency of thereadout device. Each qubit device can have two or more nearest-neighborqubit devices in the multi-dimensional array, and the qubit operatingfrequency of each qubit device can be distinct from the respective qubitoperating frequencies of each nearest-neighbor qubit device. The quantumcomputing method can include producing qubit readout signals at readoutdevices associated with the multi-dimensional array of qubit devices.Each readout device can be operably coupled to a single, respectivequbit device. Each qubit readout signal can be produced by one of thereadout devices based on an electromagnetic interaction between thereadout device and the respective qubit device. The quantum computingmethod can include receiving coupler control signals at coupler devices.The coupler devices can reside at intervals between neighboring pairs ofthe qubit devices in the multi-dimensional array. The coupler controlsignal received by each coupler device can be configured to produce anelectromagnetic interaction between the neighboring pair of qubitdevices that the coupler device resides between. The quantum computingmethod can include manipulating a coupling strength of theelectromagnetic interactions produced by the respective coupler devicesby controlling offset electromagnetic fields experienced by therespective coupler devices.

In a general aspect of what is described above, a quantum computingmethod includes generating quantum processor control information for agroup of devices housed in a quantum processor cell. Each device in thegroup has a distinct operating frequency. A multiplexed control signalis generated based on the quantum processor control information. Themultiplexed control signal is communicated on a physical channel into aninput signal processing system. Device control signals are separatedfrom the multiplexed control signal by de-multiplexing the multiplexedcontrol signal in the input signal processing system. The respectivedevice control signals are communicated into the quantum processor cellfor the group of devices.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The quantum computingmethod can include communicating the multiplexed control signal from afirst, higher temperature stage to a second, lower temperature stage,wherein the input signal processing system and the quantum processorcell operate in the second temperature stage. The first temperaturestage can be a room temperature stage, and the second temperature stagecan be a cryogenic temperature stage. The quantum computing method caninclude de-multiplexing the multiplexed control signal in a low-noise,cryogenic environment. The multiplexed control signal can be a microwavesignal communicated by a microwave transmission line. The quantumcomputing method can include shielding the quantum processor cellagainst microwave and optical frequencies. The shielding can beperformed by metallic, superconducting, or lossy material, or acombination thereof. The quantum processor control information caninclude control sequences for the respective devices in the group. Eachdevice control signal can correspond to one of the control sequences.The control sequences can include digital information, and the devicecontrol signals can be analog information. The quantum computing methodcan include: receiving, at an output signal processing system, qubitreadout signals from a group of readout devices housed in a quantumprocessor cell; generating a multiplexed readout signal in the outputsignal processing system by multiplexing the qubit readout signals; andcommunicating the multiplexed readout signal from the output signalprocessing system on a physical channel. The quantum computing methodcan include: generating multiplexed control information from the quantumprocessor control information; and generating a multiplexed controlsignal from the multiplexed control information. The quantum processorcontrol information can include digital information generated byoperation of one or more processors executing computer-readableinstructions, and the multiplexed control signal can include an analogsignal generated by a waveform generator. Communicating the respectivedevice control signals into the quantum processor cell can includecommunicating each device control signal from the input signalprocessing system to a respective input interconnect signal line. Eachof the input interconnect signal lines can extend from an exterior ofthe quantum processor cell to an interior of the quantum processor cell.The quantum computing method can include routing the device controlsignals to the respective devices within the quantum processor cell. Thegroup of devices can be supported in the quantum processor cell by asignal board that includes signal lines. The device control signals canbe routed to the respective devices by the signal lines. The group ofdevices can be a group of qubit devices. The quantum processor controlinformation can include qubit control information for the group of qubitdevices. The qubit control information can include qubit controlsequences for the respective qubit devices in the group, and the qubitcontrol sequence for each qubit device can be configured to execute asingle-qubit operation on the qubit device. The group of devices can bea group of coupler devices. The quantum processor control informationcan include coupler control information for the group of couplerdevices. The coupler control information can include coupler controlsequences for the respective coupler devices in the group, and thecoupler control sequence for each coupler device can be configured toexecute a two-qubit operation on a pair of qubit devices that neighborthe coupler device. The group of devices can be a group of readoutdevices. The quantum processor control information can include readoutcontrol information for the group of readout devices. The readoutcontrol information can include readout control sequences for therespective readout devices in the group, and the readout controlsequence for each readout device can be configured to execute a readoutoperation of a qubit device associated with the readout device. Thegroup of devices can be a first group of devices that each have distinctoperating frequencies in a frequency range, and the method can include:generating first quantum processor control information for the firstgroup of devices; generating second, distinct quantum processor controlinformation for a second group of devices housed in a quantum processorcell; generating a first multiplexed control signal based on the firstquantum processor control information; generating a second, distinctmultiplexed control signal based on the second quantum processor controlinformation; communicating the first multiplexed control signal on afirst physical channel into the input signal processing system;communicating the second multiplexed control signal on a second,distinct physical channel into the input signal processing system;separating a first set of device control signals from the firstmultiplexed control signal by de-multiplexing the first multiplexedcontrol signal in the input signal processing system; separating asecond, distinct set of device control signals from the secondmultiplexed control signal by de-multiplexing the second multiplexedcontrol signal in the input signal processing system; communicating thefirst set of device control signals into the quantum processor cell forthe first group of devices; and communicating the second set of devicecontrol signals into the quantum processor cell for the second group ofdevices. The quantum processor cell can include a multi-dimensionalarray of qubit devices. The multi-dimensional array can includesub-arrays associated with separate frequency bands. The qubit devicesin each sub-array can have a qubit operating frequency within thefrequency band associated with the sub-array. The group of devices canbe a group of the qubit devices in the multi-dimensional array, and thegroup of qubit devices can include one qubit device in each of thesub-arrays. The multi-dimensional array includes multiple groups ofqubit devices, and each group of qubit devices can include one qubitdevice in each of the sub-arrays.

In a general aspect of what is described above, a quantum computingsystem includes a control system and an input signal processing system.The control system includes one or more data processors and a waveformgenerator. The input signal processing system includes an input channel,a de-multiplexer and output channels.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The one or more dataprocessors are configured to generate quantum processor controlinformation for a group of qubit devices housed in a quantum processorcell. Each device in the group has a distinct operating frequency. Thewaveform generator is configured to generate a multiplexed controlsignal from the quantum processor control information. The waveformgenerator can be an arbitrary waveform generator configured to convertdigital signals to analog signals. The input channel is configured toreceive the multiplexed control signal. The de-multiplexer is configuredto separate device control signals from the multiplexed control signal.The output channels are configured to communicate the respective devicecontrol signals into the quantum processor cell for the group ofdevices. The control system can be configured to operate at a first,higher temperature stage, and the input signal processing system and thequantum processor cell can be configured to operate at a second, lowertemperature stage. The first temperature stage can be a room temperaturestage, and the second temperature stage can be a cryogenic temperaturestage. The input signal processing system can be configured to processdevice control signals in a low-noise, cryogenic environment. Thequantum computing system can include magnetic shielding material aboutthe quantum processor cell and the input signal processing system. Themultiplexed control signal can be a microwave signal, and the quantumcomputing system can include a microwave transmission line configured tocommunicate the multiplexed control signal. The quantum processorcontrol information can include control sequences for the respectivedevices in the group, and each device control signal can corresponds toone of the control sequences. The control system can be configured togenerate digital information that defines the control sequences, and thewaveform generator can be configured to generate analog information thatdefines the multiplexed control signal. The input signal processingsystem can include a board that supports processing cards. Theprocessing cards can be supported in receptacle slots defined in theboard. The input signal processing system can include multiple inputprocessing domains. Each input processing domain can include arespective subset of the processing cards. At least one of theprocessing cards in each input processing can be interchangeable with acorresponding processing card in another input processing domain. Thequantum computing system can include an output signal processing systemthat includes: input channels configured to receive qubit readoutsignals from the group of devices; a multiplexer configured to generatea multiplexed readout signal by multiplexing the qubit readout signals;and an output channel configured to communicate the multiplexed readoutsignal from the output signal processing system. The quantum computingsystem can include an input interconnect system that includes inputinterconnect signal lines extending from an exterior of the quantumprocessor cell to an interior of the quantum processor cell. The inputinterconnect signal lines can be configured to communicate the devicecontrol signals between the output channels and the respective devices.The input interconnect system can include plateau structures thatsupport at least a portion of the input interconnect signal lines insidethe quantum processor cell. The quantum computing system can include asignal board that supports the devices in the quantum processor cell andincludes signal lines. The signal lines can be configured to route thedevice control signals within the quantum processor cell to therespective devices. The group of devices can be a group of qubitdevices. The quantum processor control information can include qubitcontrol information for the group of qubit devices. The group of devicescan be a group of coupler devices. The quantum processor controlinformation can include coupler control information for the group ofcoupler devices. The group of devices can be a group of readout devices.The quantum processor control information can include readout controlinformation for the group of readout devices. The quantum processor cellcan include a multi-dimensional array of qubit devices. Themulti-dimensional array can include sub-arrays associated with separatefrequency bands. The qubit devices in each sub-array can have a qubitoperating frequency within the frequency band associated with thesub-array. The group of devices can include a group of the qubit devicesin the multi-dimensional array. The group of qubit devices can includeone qubit device in each of the sub-arrays. The multi-dimensional arraycan include multiple groups of qubit devices. Each group of qubitdevices can include one qubit device in each of the sub-arrays.

In a general aspect of what is described above, a quantum computingmethod includes receiving, at an output signal processing system, qubitreadout signals from a group of readout devices housed in a quantumprocessor cell. A multiplexed readout signal is generated in the outputsignal processing system by multiplexing the qubit readout signals. Themultiplexed readout signal is communicated from the output signalprocessing system on a physical channel. The multiplexed readout signalis received at a control system. Qubit readout data are identified, byoperation of the control system, from each readout device. The qubitreadout data for each respective readout device are identified from themultiplexed readout signal based on the distinct readout frequency ofthe readout device. Based on qubit readout data, multiplexed quantumprocessor control information is generated for the quantum processorcell.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The quantum computingmethod can include communicating the multiplexed readout signal from afirst, lower temperature stage to a second, higher temperature stage.The output signal processing system and the quantum processor cell canoperate in the first temperature stage, and the control system canoperate in the second temperature stage. The first temperature stage canbe a cryogenic temperature stage, and the second temperature stage canbe a room temperature stage. The quantum computing method can includemultiplexing the qubit readout signals in a low-noise, cryogenicenvironment. The quantum computing method can include shielding thequantum processor cell against microwave and optical frequencies. Theshielding is performed by a metallic, superconducting, or lossymaterial, or a combination thereof. The quantum computing method caninclude: generating an analog multiplexed readout signal in the outputsignal processing system by multiplexing the qubit readout signals;communicating the analog multiplexed readout signal from the outputsignal processing system on a physical channel; generating a digitalmultiplexed readout signal by digitizing the analog multiplexed readoutsignal; and identifying, by operation of the control system, the qubitreadout data from the digitized multiplexed readout signal. The qubitreadout data for each respective device can correspond to the qubitreadout signal from the device. The qubit readout data can includedigital information, and the qubit readout signals can include analoginformation. The quantum computing method can include: generating amultiplexed control signal based on the multiplexed quantum processorcontrol information; communicating the multiplexed control signal on aphysical channel into an input signal processing system; separatingdevice control signals from the multiplexed control signal byde-multiplexing the multiplexed control signal in the input signalprocessing system; and communicating the respective device controlsignals into the quantum processor cell for the group of devices. Thequbit readout data can include digital information, and the multiplexedreadout signal can include analog information. The quantum computingmethod can include communicating the qubit readout signals from therespective devices to the output signal processing system. Each qubitreadout signal can be communicated to the output signal processingsystem by a respective output interconnect signal line. Each of theoutput interconnect signal lines can extends from an interior of thequantum processor cell to an exterior of the quantum processor cell. Thequantum computing method can include routing the qubit readout signalsfrom the devices to the output interconnect signal lines within thequantum processor cell. The group of devices can be supported in thequantum processor cell by a signal board that includes the signal lines.The qubit readout signals can be routed from the respective devices bythe signal lines. The quantum computing method can include obtaining thequbit readout signals by operation of the readout devices in the quantumprocessor cell. Each of the readout devices can be operatively coupledto a respective qubit device in the quantum processor cell. The quantumprocessor control information can include coupler control informationfor a group of coupler devices in the quantum processor cell. Thecoupler control information can include coupler control sequences forthe respective coupler devices in the group, and the coupler controlsequence for each coupler device can be configured to execute atwo-qubit operation on a pair of qubit devices that neighbor the couplerdevice. The quantum processor cell can house a group of qubit devices.Each of the readout devices can be operably coupled to a single,respective one of the qubit devices. The qubit readout signal producedby each readout device can indicates a state of the qubit device towhich the readout device is operably coupled. The group of readoutdevices can include a first group of readout devices that each havedistinct operating frequencies in a frequency range. The quantumcomputing method can include: receiving, at the output signal processingsystem, first qubit readout signals from the first group of readoutdevices; receiving, at the output signal processing system, second,distinct qubit readout signals from a second, distinct group of readoutdevices housed in the quantum processor cell, the second group eachhaving distinct operating frequencies in the frequency range; generatinga first multiplexed readout signal in the output signal processingsystem by multiplexing the first qubit readout signals; generating asecond, distinct multiplexed readout signal in the output signalprocessing system by multiplexing the second qubit readout signals;communicating the first multiplexed readout signal from the outputsignal processing system on a first physical channel; communicating thesecond multiplexed readout signal from the output signal processingsystem on a second, distinct physical channel; receiving the first andsecond multiplexed readout signals at the control system; identifying,by operation of the control system, qubit readout data from each readoutdevice in the first and second groups, the qubit readout data for eachrespective readout device identified from the first and secondmultiplexed readout signals based on the distinct readout frequency ofthe readout device; and based on qubit readout data, preparing themultiplexed quantum processor control information for the quantumprocessor cell. The quantum processor cell can include amulti-dimensional array of qubit devices. The multi-dimensional arraycan include sub-arrays associated with separate frequency bands. Thequbit devices in each sub-array can have a qubit operating frequencywithin the frequency band associated with the sub-array. The qubitreadout signals can be associated with a group of the qubit devices inthe multi-dimensional array, and the group of qubit devices can includeone qubit device in each of the sub-arrays.

In a general aspect of what is described above, a quantum computingsystem includes an output signal processing system and a control system.The output signal processing system includes input channels, amultiplexer and an output channel. The control system includes one ormore data processors.

Implementations of any of the general aspects described in this documentmay include one or more of the following features. The input channelsare configured to receive qubit readout signals from a group of readoutdevices housed in a quantum processor cell. Each readout device in thegroup has a distinct readout frequency. The multiplexer is configured togenerate a multiplexed readout signal by multiplexing the qubit readoutsignals. The output channel is configured to communicate the multiplexedreadout signal from the output signal processing system. The one or moredata processors are operable to receive the multiplexed readout signal.The one or more data processors are operable to identify, from themultiplexed readout signal, qubit readout data for each qubit device inthe group based on the distinct readout frequency of the readout deviceThe one or more data processors are operable to prepare multiplexedquantum processor control information for the quantum processor cellbased on the qubit readout data. The control system can be configured tooperate at a first, higher temperature stage. The output signalprocessing system and the quantum processor cell can be configured tooperate at a second, lower temperature stage. The first temperaturestage can be a room temperature stage, and the second temperature stagecan be a cryogenic temperature stage. The output signal processingsystem can be configured to process device control signals in alow-noise, cryogenic environment. The quantum computing system caninclude magnetic shielding material about the quantum processor cell andthe output signal processing system. The qubit readout data for eachrespective device can corresponds to the qubit readout signal from thedevice. The output signal processing system can include a board thatsupports processing cards. The processing cards can be supported inreceptacle slots defined in the board. The output signal processingsystem can include multiple output processing domains. Each outputprocessing domain can include a respective subset of the processingcards. At least one of the processing cards in each output processingdomain can be interchangeable with a corresponding processing card inanother output processing domain. The quantum computing system caninclude a waveform generator configured to generate a multiplexedcontrol signal from the multiplexed quantum processor controlinformation and an input signal processing system. The input signalprocessing system can include: an input channel configured to receivethe multiplexed control signal; a de-multiplexer configured to separatedevice control signals from the multiplexed control signal; and outputchannels configured to communicate the respective device control signalsinto the quantum processor cell. The quantum computing system caninclude an output interconnect system that includes output interconnectsignal lines extending from an interior of the quantum processor cell toan exterior of the quantum processor cell. The output interconnectsignal lines can be configured to communicate the qubit readout signalsbetween the readout devices and the respective input channels of theoutput signal processing system. The output interconnect system caninclude plateau structures that support at least a portion of the outputinterconnect signal lines inside the quantum processor cell. The quantumcomputing system can include a signal board that supports the devices inthe quantum processor cell and includes signal lines. The signal linescan be configured to route the qubit signals within the quantumprocessor cell from the respective readout devices. The quantumcomputing system can include the quantum processor cell and a group ofqubit devices housed in the quantum processor cell. Each qubit devicecan have a respective qubit operating frequency. Each of the readoutdevices can be operably coupled to a single, respective one of the qubitdevices. The qubit readout signal produced by each readout device canindicate a state of the qubit device to which the readout device isoperably coupled. The quantum processor cell can include amulti-dimensional array of qubit devices. The multi-dimensional arraycan include sub-arrays associated with separate frequency bands. Thequbit devices in each sub-array can have a qubit operating frequencywithin the frequency band associated with the sub-array. The qubitreadout signals can be associated with a group of the qubit devices inthe multi-dimensional array. The group of qubit devices can includes onequbit device in each of the sub-arrays. The output signal processingsystem can include filters, circulators and quantum amplifiersconfigured to process the qubit readout signals.

While this specification contains many details, these should not beconstrued as limitations on the scope of what may be claimed, but ratheras descriptions of features specific to particular examples. Certainfeatures that are described in this specification in the context ofseparate implementations can also be combined. Conversely, variousfeatures that are described in the context of a single implementationcan also be implemented in multiple embodiments separately or in anysuitable subcombination.

A number of examples have been described. Nevertheless, it will beunderstood that various modifications can be made. Accordingly, otherimplementations are within the scope of the following claims.

1-73. (canceled)
 74. A quantum computing system comprising: a quantumprocessor cell comprising a multi-dimensional array of qubit devices,the multi-dimensional array comprising sub-arrays associated withseparate frequency bands, the qubit devices in each sub-array having aqubit operating frequency within the frequency band associated with thesub-array; and a signal delivery system communicably coupled between thequantum processor cell and a control system, the signal delivery systemconfigured to transfer signals between the array of qubit devices andthe control system.
 75. The quantum computing system of claim 74,wherein: the frequency bands are spaced apart from each other byintervals along a frequency spectrum, and at least one of the frequencybands is spaced by a first interval from the nearest-neighbor frequencyband in a first direction in the frequency spectrum, and is spaced by asecond, distinct interval from the nearest-neighbor frequency band in asecond direction in the frequency spectrum.
 76. The quantum computingsystem of claim 74, wherein: the frequency bands are spaced apart fromeach other by intervals along a frequency spectrum, and the intervalsbetween neighboring pairs of frequency bands include a first subset ofequal intervals and a second subset of equal intervals, the intervals inthe first subset being larger than the intervals in the second subset.77. The quantum computing system of claim 74, wherein themulti-dimensional array includes groups of the qubit devices, each groupincludes one qubit device in each of the sub-arrays, the groupscollectively define a tiling over the multi-dimensional array. 78-80.(canceled)
 81. The quantum computing system of claim 74, a wherein themulti-dimensional array includes groups of the qubit devices, each groupincludes one qubit device in each of the sub-arrays, and the controlsystem comprises one or more waveform generator systems configured togenerate multiplexed control signals for each respective group of thequbit devices.
 82. The quantum computing system of claim 81, wherein thesignal delivery system comprises an input signal processing system thatincludes, for each group of qubit devices: an input channel configuredto receive the multiplexed control signal for the group of qubitdevices; a de-multiplexer configured to separate device control signalsfrom the multiplexed control signal for the group of qubit devices; andoutput channels configured to communicate the respective device controlsignals into the quantum processor cell for the group of qubit devices.83. The quantum computing system of claim 82, wherein the signaldelivery system comprises an output signal processing system thatincludes, for each group of qubit devices: input channels configured toreceive qubit readout signals from a group of readout devices associatedwith the group of qubit devices; a multiplexer configured to generate amultiplexed readout signal by multiplexing the qubit readout signals;and an output channel configured to communicate the multiplexed readoutsignal from the output signal processing system on a physical channel.84. The quantum computing system of claim 83, wherein the control systemcomprises one or more data processors operable to: receive themultiplexed readout signal for each group of readout devices; andidentify, from each multiplexed readout signal, qubit readout data foreach qubit device in the group based on the readout frequency of theassociated readout device.
 85. The quantum computing system of claim 74,a wherein each qubit device has two or more nearest-neighbor qubitdevices in the multi-dimensional array, and the qubit operatingfrequency of each qubit device is distinct from the respective qubitoperating frequencies of each nearest-neighbor qubit device.
 86. Thequantum computing system of claim 74, a comprising readout devicesassociated with the multi-dimensional array of qubit devices, eachreadout device operably coupled to a single, respective qubit device andconfigured to produce a qubit readout signal that indicates a state ofthe respective qubit device.
 87. The quantum computing system of claim74, a comprising coupler devices residing at intervals betweenneighboring pairs of the qubit devices in the multi-dimensional array,each coupler device being configured to produce an electromagneticinteraction between the respective neighboring pair of qubit devicesthat the coupler device resides between.
 88. The quantum computingsystem of claim 87, wherein the electromagnetic interaction produced byeach coupler device has a coupling strength that varies with an offsetelectromagnetic field experienced by the coupler device.
 89. The quantumcomputing system of claim 87, wherein each neighboring pair of qubitdevices comprises a first qubit device having a first qubit operatingfrequency and a second qubit device having a second, distinct qubitoperating frequency.
 90. The quantum computing system of claim 87,wherein the multi-dimensional array defines a first set of intervalsalong a first dimension of the array and a second set of intervals alonga second dimension of the array, a first subset of the coupler devicesreside at the first set of intervals, and a second subset of the couplerdevices reside at the second set of intervals. 91-92. (canceled)
 93. Thequantum computing system of claim 74, a comprising an electromagneticwaveguide system, the electromagnetic waveguide system comprising aninterior surface that defines an interior volume of intersectingwaveguides, wherein the qubit devices are housed in the electromagneticwaveguide system.
 94. The quantum computing system of claim 93, whereinthe intersecting waveguides each define a cutoff frequency and isconfigured to evanesce electromagnetic waves below the cutoff frequency,and the qubit operating frequency of each qubit device is below thecutoff frequencies.
 95. The quantum computing system of claim 94,wherein the interior surface defines waveguide cross-sections, and thecutoff frequencies are defined by the waveguide cross-sections.
 96. Aquantum computing method comprising: receiving qubit control signals ata quantum processor cell comprising a multi-dimensional array of qubitdevices, the multi-dimensional array comprising sub-arrays associatedwith separate frequency bands, the qubit devices in each sub-arrayhaving a qubit operating frequency within the frequency band associatedwith the sub-array, the qubit control signal received by each qubitdevice being configured to manipulate a quantum state of the qubitdevice; and communicating the qubit control signals to respective qubitdevices in the quantum processor cell.
 97. The quantum computing methodof claim 96, wherein: the frequency bands are spaced apart from eachother at intervals along a frequency spectrum, and at least one of thefrequency bands is spaced by a first interval from the nearest-neighborfrequency band in a first direction in the frequency spectrum, and isspaced by a second, distinct interval from the nearest-neighborfrequency band in a second direction in the frequency spectrum.
 98. Thequantum computing method of claim 96, wherein: the frequency bands arespaced apart from each other at intervals along a frequency spectrum,and the intervals between neighboring pairs of frequency bands include afirst subset of equal intervals and a second subset of equal intervals,the intervals in the first subset being larger than the intervals in thesecond subset.
 99. The quantum computing method of claim 96, wherein themulti-dimensional array includes groups of the qubit devices, each groupincludes one qubit device in each of the sub-arrays, and the groupscollectively define a tiling over the multi-dimensional array.
 100. Thequantum computing method of claim 99, wherein the multi-dimensionalarray comprises a two-dimensional array, and the tiling comprises atwo-dimensional tiling.
 101. The quantum computing method of claim 96,wherein the multi-dimensional array includes groups of the qubitdevices, each group includes one qubit device in each of the sub-arrays,and the method comprises, for each respective group of the qubitdevices: generating qubit control information; generating a multiplexedcontrol signal from the qubit control information; communicating themultiplexed control signal on a physical channel into an input signalprocessing system; separating qubit control signals from the multiplexedcontrol signal by de-multiplexing the multiplexed control signal in theinput signal processing system; and communicating the respective qubitcontrol signals into the quantum processor cell.
 102. The quantumcomputing method of claim 96, wherein the multi-dimensional arrayincludes groups of the qubit devices, each group includes one qubitdevice in each of the sub-arrays, and the method comprises, for eachrespective group of the qubit devices: producing qubit readout signalsby operating a group of readout devices associated with the group ofqubit devices, the group of readout devices having respective readoutfrequencies; generating a multiplexed readout signal in an output signalprocessing system by multiplexing the qubit readout signals;communicating the multiplexed readout signal from the output signalprocessing system on a physical channel; receiving the multiplexedreadout signal at a control system; and identifying, by operation of thecontrol system, qubit readout data for each device in the group, thequbit readout data from each respective readout device identified fromthe multiplexed readout signal based on the readout frequency of thereadout device.
 103. The quantum computing method of claim 96, whereineach qubit device has two or more nearest-neighbor qubit devices in themulti-dimensional array, and the qubit operating frequency of each qubitdevice is distinct from the respective qubit operating frequencies ofeach nearest-neighbor qubit device.
 104. The quantum computing method ofclaim 96, comprising producing qubit readout signals at readout devicesassociated with the multi-dimensional array of qubit devices, eachreadout device operably coupled to a single, respective qubit device,each qubit readout signal produced by one of the readout devices basedon an electromagnetic interaction between the readout device and therespective qubit device.
 105. The quantum computing method of claim 96,comprising receiving coupler control signals at coupler devices, thecoupler devices residing at intervals between neighboring pairs of thequbit devices in the multi-dimensional array, the coupler control signalreceived by each coupler device being configured to produce anelectromagnetic interaction between the neighboring pair of qubitdevices that the coupler device resides between.
 106. The quantumcomputing method of claim 105, comprising manipulating a couplingstrength of the electromagnetic interactions produced by the respectivecoupler devices by controlling offset electromagnetic fields experiencedby the respective coupler devices.
 107. (canceled)